Planning our first time to London: please post your top "must-sees" and why.

Be very careful about taking seeds home without a phytosanitary certificate.

APHIS has strict regulations on importation of even small amounts of seed.

http://www.aphis.usda.gov/wps/portal/aphis/ourfocus/planthealth/saimport/sapermits/saplantplantproducts/saplantsforplanting/ctplantsforplantinghome/!ut/p/a1/lVNRj6IwEP41PGJHQIF9Q9cTdd3d3GWj8kJKLbQRWq4Ujf9-K5o7L3F1rwNdOZr55v5pihBa5QIvOcF1lwKXJ7OyTCdv8VOfwTObDqdjGD2-uPl3VMHVgODGBzB7AYfO-eBrFnv8CAF7gwOx5FD74RJgNnx0f4USlBCha83QBteMNymRQlOh05JnCqujBQ1OZavSXJK26U51iU2cUVxq1jl4VUulzzGqKq6vcZddyW1LrgONeVGdTS4KC4i-5U-ZrOiJZE341lAknjdwfWqHYeDZXp6DHeZO34YhhJ7r9h3Hg0tT4IsVwbea8kCWDnCv7x3gDoeNIelmWIyRL-s-r5w7LGKInb-Pg7OnXIUcvxsjAZsGY2F7lE6z9KduZFybN9Q8mgX8VQ-t7ShqWRSmz7m9sIpG5geGgaE4VVb1WGTfTun6ywILD4dAjWd0r5N4CrfCelhZwM5xKXP6XvecN11KZqdplRzNDhhvjGdd0ayvaaMWJMW9lYrIxVV5lQHX18VEF7tHeQzAHexW0Xu1CproEwwDhxM!/?1dmy&urile=wcm%3apath%3a%2Faphiscontentlibrary%2Fsaourfocus%2Fsaplanthealth%2Fsaimport%2Fsapermits%2Fsaplantplantproducts%2Fsaplantsforplanting%2Fctpermitplantmaterials

or search USDA for "What Plant Material Requires a Permit?".

For first timers and given your preferences, believe think these places would meet your travel criteria: http://www.bl.uk/events/treasures-of-the-british-library. Self explanatory if you peruse the link.
Instead of the castles you've listed visit Henry VIII's Hampton Court. Can train to and cruise back, or vice versa, makes a nice day out. Liberty Dartment store. Once you walk through the doors you'll understand why. History abounds in Westminster Abbey so please make an effort to visit it. U mentioned something unique, check out Richard Branson's rooftop garden. Free of charge.
virginlimitedadditon.com I'd also checkout the Original London walks and see if any are of interest to you. www.walks.com. Nice way to learn about London's history. Get tickets for a play at the Globe theatre. I'd not miss the fun and flair of Camden Lock Market nor the opportunity to walk along the adjacent canal. I always tell friends to visit Leadenhall Market. It's glass covered and the surrounding modern buildings define the city's dichotomy. Old and new. As far as unusual spots, Mudchute farm, the lullaby factory (a musical art installation) at the Great Ormond Street Hospital, the Blackfriar pub, and the Hunterian Museum, ( body parts and surgical instruments). More than enough to keep you occupied and as its May I'd picnic in Hyde Park, Regent's park or the Hampstead Heath. Great city. Enjoy it.

Kew Gardens has a WONDERFUL shop. We've brought home many packets of flower seeds over the years. They also have some of the best souvenirs! Unfortunately, we haven't been in quite a few years, but last time we went there was still a wonderful little garden shop in the village itself- right along the way you walk from the station to the gardens.

Instead of an Oyster, consider buying a travel card from a National Rail Station (Paddington is one) and using the 2-for-1 deals offered by Transport For London (TfL). Even if you buy a 7 day card, you may save more than you'd spend on it. Check it out here [http://www.daysoutguide.co.uk/london-transport-museum][1]

Additionally, Windsor Castle and Windsor itself, is one of our favorite places. Easy to get to from Paddington by rail (about a 25-30 min. journey with one change at Slough). We often go there in the morning and head back around 3 ish on days when we have theatre tickets for the evening. Trains run every 20-30 min, so its easy to just head on back when you decide you're done.

Other day trips to consider (all easy to do by rail)- Cardiff Wales, Winchester, York, Stratford-upon-Avon, Brighton, Canterbury, Dover, and many others.

Top London sights:
1. Tower Of London
2. Westminster Abbey
3. The British Museum
4. St. Paul's Cathedral
5. Shakespeare's Globe Theatre
6. The British Library
7. The Victoria and Albert Museum (the V&A)
8. National Portrait Gallery
9. Walk by/over Tower Bridge
10. Hampton Court Palace (out of town by train)
11. Windsor Castle (out of town by train)

You asked for the top sights "and why". Because going to all of these sights will teach you the history of England, in detail.

When you are out of town on your Cotswolds/Oxford/Blenheim leg of the trip, with a car, consider going to see Warwick Castle. A bit out of the way, but worth it.

Westminster Abbey, the Churchill War Rooms, the Tower of London, Tower Bridge, Rick Steve's East End Walk, City Walk, Westminster Walk, and West End Walk, the British Museum, National Gallery, British Library, and on and on. Take your pick.

Not sure about the castle tours, sorry.

Google "The Cabinet War Rooms" and see if it interest you. It is the place from which Britain directed their efforts during WWII. Tremendous bit of history there. TC

1) The British Museum ...for the history of the world!
2) Tower of London...for English history with fun, informative beefeater tour guides
3) Westminster Abbey...the most amazing church, where the hundreds/thousands entombed: kings, queens, poets, scientists, politicians

I cannot help but recommend dropping by the most famous crosswalk in the world outside Abbey Road Studios.

I would second the London walks, they are amazing and worth every penny. I think you need to see the British museum and British library, Rick Steves does an audio tour of both if you have smart phones (I like them because they pick out the 'good stuff' before I get overwhelmed). I thought that the Churchill war rooms were interesting and would love to see the Imperial War Museum but it was closed for renovations when I was there. I think that seeing some theatre is also great if you are interested in it and don't live somewhere like New York where there is a lot of live theatre. We get some traveling shows through Iowa but nothing with the sets I saw at Wicked.

Staying near Paddington you really should consider going to Little venice and take a boat to Camden Lock markets and/or the Zoo (http://www.jasons.co.uk/ or http://www.londonwaterbus.co.uk/)

We loved Hampton Court....the tour of the kitchens was sooo interesting! Highlights for us also included: Tower of London (the Beefeater guides are exceptional!) , British Museum, St. Paul's Cathedral and Westminster Abbey. We did go to the Imperial War Museum but found it did not meet our expectations.....felt rather contrived and off the mark (IMO). We had absolutely no trouble getting around on the tube (and we are from Vancouver, Canada so no experience with that kind of transportation!). Enjoy your trip!

I would really do your research on bringing home seeds. In April 2010 I brought home "Shakespeare's Seeds" that I bought in a tourist shop in Stratford Upon Avon. When I arrived in the US I was pulled out of the Customs Line by an officer. It was a humiliating experience. They took my seeds and opened my bag searching through, etc. I couldn't keep my seeds and everyone stared at me. They also told me that they were being "nice" because they were not going to give me a big fine this time like they normally would. So please do your research.

As a gardener, you might want to check out the Columbia Road Flower Market on Sunday mornings. My mom is also a gardener and she loved it!

As for something different mixed in with local history, try a Mudlarking tour with some beachcombing by the Thames--London Walks provides a guided tour to help you determine what it is you're finding on the shore.

Tower of London for its historical significance and sheer magnitude of things to see. Westminster Abbey for its beauty, famous tombs, and significance.

also don't miss strolling in Hyde Park and the adjacent Kensington garden. So important to London and both are such a beautiful place.

I saw all the top must-sees in London/area and of them, here are my favorites:

1. Portobello Road market on a Saturday morning--I first read the Paddington books when I was 8 and thus for over 35 years I knew I needed to visit London and that I had to visit the market since I love antiques and flea markets and it has quite a variety of everything.

2. Windsor Castle because of the fabulous Queen Mary's Dolls' House, lovely grounds and charming town of Windsor itself.

3. Churchill War Rooms and Museum--part of the Imperial War Museum, a must-see because I am fascinated by the man and interested in WWII history and you really get the feeling when in the underground rooms that the war just ended and everything was left as it lay 60 years ago.

4. Westminster Abbey--Poet's Corner was enough to thrill me but the entire church and grounds are beautiful and interesting. Big Ben and Parliament are right there and it's a 5 minute walk to the Churchill Museum.

5. British Library--Perhaps just for fans of British literature, but the Magna Carta is there and I got to see other delights such as Charlotte Bronte's handwritten draft of Jane Eyre's last chapter: "Reader, I married him."

Might pass you somewhere - we'll be in London around the same time! Ours: Tower of London; London Bridge; Crown Jewels; Westminster Abbey and Cathedral; really would like to watch changing of guard at Buckingham Palace - anyone know how often it's done? I know - I haven't looked.... We're also going to Windsor Castle - after an excursion out into the country side to visit a family history related area. Would LOVE to do the museums - but don't think we'll have time!

Tower Bridge:
http://www.suffolkcoastsailing.co.uk/_wp/wp-content/uploads/2014/04/tower-bridge1.jpg

London Bridge (not interesting at all):
http://www.walklondon.com/london-walks/walk-london-images/pool-of-london/london-bridge-att3.jpg