One full day to see a little of London- most efficient plan?

London is a very walkable city. You can map out your own walk based on your specific interests. If you like "Junque" go to one of the street markets open Saturday very early in the morning. Look up London Street Markets. You can also walk by Buckingham Palace and Westminster and Big Ben. Visit the Tower of London! You may have to make reservations. Ride River Thames. Walk along the river to look at many monuments. Visit the British Museum! Visit the National Gallery! Visit the Tate! Visit the Library! Go to a Pub and have dinner.

I think if walking a lot is an issue then a hop on hop off bus is a very good option to give you a good overview of London as you've never been before and you have limited time. It's very easy to do a LOT of walking while in London. I would focus on just a couple of main sights like Westminster Abbey and the Tower of London.

Find your hotel on a map. If it's near the east end of Hyde Park, it should be a pretty easy walk through Mayfair and St. James's to Trafalgar Square, down Whitehall to the Abbey and Parliament, maybe back through St. James's Park to Buckingham Palace or maybe across the river and along the south bank till you're ready to cross again. The sights are very spread out so you won't see "everything" on foot, but you'll certainly get a good feel for the city's layout. When you're plumb worn out, get on the Tube and head back to the hotel or someplace for dinner.

The Tube is very fast (crowded at rush hours), the buses are slower but you can see a lot from them, especially the upper deck. The Benson's map shows bus routes. Maybe you'll want to make a short list of sights you want to visit, and try to get between them on buses so you take in the streets while (hopefully) sitting down. Maybe you'll want to take the tube from near your hotel (especially if it's north, south, or west of Hyde Park) to the Westminster stop, or Trafalgar Square, and start your walking tour from there.

A day and a half will give you a feel for the city's layout and atmosphere, and a chance to see a few places in more depth. Hopefully the weather will cooperate.

With your situation I would definitely consider the hop on/hop off bus. I've not done it in London, but I believe it includes a boat ride on the Thames.

Here's the plan.

If your hotel has breakfast, enjoy it. If not and you like to walk there are two lovely cafes in Hyde Park that I enjoy getting coffee and a nosh at. If staying on the North side of Hyde Park near Lancaster Gate Station walk into the park at the Italian Gardens.
Entrance right across Bayswater road. Immediately to your left is a small cafe with pastries and coffee OR do what I do and continue walking into the park towards the Princess Diana Memorial Fountain to the cafe near the Lido. Beautiful walk. Tables and chairs inside and outside. Have breakfast watching the water fowl and early morning swimmers. FYI The Memorial fountain opens at 10am.

Then walk to the nearest tube station. Walk up to the manned ticket booth and purchase a day travel card for each of you. Explain that you are only in London for a day and a half and only seeing sites within Zone 2.

Look at the large tube map posted on the wall and find the Westminster stop. North side of Hyde Park are Lancaster Gate and Queensway station and on the south Knightsbridge and Hyde Park corner.

If you are on the North side then you will be taking the Red Central Line train to Bond Street and changing to the Grey Jubilee line train to Westminster Station. If you are on the South side its the Dark Blue Piccadilly line to Green Park where you will get on the Grey Jubilee line. Exit the station and you will be in Parliament Square (Parliament, Big Ben, Westminster Abbey, Churchill War Rooms). You will need to decide before you go on your trip what you want to see. Westminster Abbey or Churchill War rooms. Both pricey and best to book advance tickets. Research. If you don't wish to go in either of them then you can walkup Birdcage Walk (there is signage) into St James Park and up to Buckingham Palace. From the palace walk through Green Park to Piccadilly (turn right) and follow it down to Piccadilly Circus. Maybe shop at Fortum and Mason?

OR from Parliament Square walk up Whitehall past the Horse Guards, 10 downing Street to Trafalgar Square and from there walk into Covent Garden.

ORafter touring Westminster Abbey or Churchill War Rooms return to Westminster Station and take the Grey Jubilee Line back to Bond Street and then take the Red Central Line train to Nottinghill Gate. Exit and take Pembridge Road up to Portobello Road and wander through the market. It's on full bore on Saturday. Closed on Sunday. http://www.portobelloroad.co.uk/the-market/

ORafter seeing Parliament Square get back on the tube and take the Grey Jubilee line to London Bridge station. Exit and follow signage to Borough Market. From there you could go to the Sky Garden at The Shard.

Its a walkable city as well. BEST way to see how close and far "sites" are is to use Google Maps Satellite POV.

If you want to use the tube and busses make use of the Transport for London website: https://tfl.gov.uk Helps you plan your journey.

So make a list of what your must see's are for the short period of time you are there, locate them on Google Maps and see what tube stations are close or if you can walk to them.

GREAT city. Enjoy it!

I haven't been London since 2001 - aside from changing planes. But when I was there, I really enjoyed riding the buses and using a map similar to this one:

http://content.tfl.gov.uk/bus-route-maps/key-bus-routes-in-central-london.pdf

Cheaper than a HOHO, and you won't have to wait long between buses. The main thing that I wanted to see on my first pleasure trip to London was Westminster Abbey. I enjoyed The Wallace Collection far more than the big name museums. It's near the Marylebone bus stop. That's where Mosley and Baxter took Daisy when they were in London for Rose's wedding - in case you watched Downton Abbey.

Since you're staying in Hyde Park, I would definitely walk over to Kensington Park and check out Kensington Palace.

Wow! So many great suggestions!

Thank you all for the invaluable information. We will dig in and do more research. I feel much more confident that we will make the best use of our time. It sounds do-able :-)

We very much appreciate getting the benefit from all your experiences.

That's a great bus map, I hadn't seen it before.

I knew you'd be all set with step-by-step ideas once Claudia saw your post! ;-)

"Slowly I turned, step by step, inch by inch...."

Yep, a walkable city.

Having done the Hop On Hop Off tour in London, I would never recommend it to another visitor. Traffic is so bad and sites are spread out enough that it really is just an overpriced time suck. Plus, a lot of the experience is dependent on your bus guide's personality and we saw how widely that varied. I fully support and enjoy the hop on hop off option in other cities, London just isn't well suited to the concept.

In our opinion, it is better to day day tours around London. We were very satisfied with Evan Evans tours. Yes, the Hop On, Hop Off is very time consuming. If you get on one like we did, there wasn't any place worthwhile to get off and turn around. It was over in the banking district. It was terrible. We have taken the Hop On, Hop Off many times, but it has its disadvantages.

Here is my strategy when I have limited time in a place. I spend time determining what interests me most about the location or what activity really interests me. I focus on the top 2-3 times on that list and let the rest go for another time.

I suggest you do the same for London. Don't go someplace or take a tour because everybody else does. First determine what is of most interest to you and do that.

The Hop on Hop Off tour drives you by many places. If that is what you want, go for it. I might suggest going ahead and picking an area or an activity to explore.

Here are some of my suggestions for possibilities:
Tower of London
Thames river cruise
Churchill War Rooms
Kensington Palace (Quite close to your hotel)
A few of the stores on Oxford Street (since you like shopping and they are close)
Aspley House (also near to Hyde Park) Home of the Duke of Wellington