10 Days In London/England/UK

I suggest using your favorite booking site to help you decide. Set the map wide (for the Cotswolds or the Kentish Coast, based on your stated interests), filter for your needs and budget, and see what you find.
If you don't want to try that hard, I can recommend a traditional B&B in Deal, which is not far from Dover and has direct train service to/from London. It's a nice, walkable town on the sea with a castle, and you can easily do a day trip to Dover by bus (or train) or to Canterbury by bus.

With just 10 days overall, and considering the intensity of London, you might want to balance out the trip by spending time west of London. There’s the Cotswolds, as G3rryCee suggests, with Blenheim Palace nearby.
Further west toward the Severn River is Bath, along with Berkeley Castle, Thornbury Castle—which is a hotel today—and just across the Severn in Wales, Chepstow Castle.

The possibilities in the UK are infinite.

Look at www.nationaltrust.org.uk for great ideas for Metropolitan London. If you've got a good weekly rate for London use it as a base for Day trips. We have spent a week in London a couple of times and we never got to see all we wanted. Use a Transit Pass and go almost everywhere. Some Museums are free. Highgate Cemetery is great fun to visit. You can take a boat one way to Hampton Court and the train back or vice versa. There are several Street Markets on different days. Check to see which ones are open in October. Of course there are Pubs, etc. Check walking tours online; don't really need a guide. I don't know if the trips to farther away Bucket List places are really worth it in October when the days are shorter and probably wetter. Look into Day Return Train Rides. Bon Voyage!

First decide what part of the UK you REALLY, really want to see. If it is reasonably close to London (less than half a day travel from London), then go there for a few days. Make sure that any nearby sites are easily reachable. Spend the rest of your time in London.

Or, if there's no particular area of interest worth several days stay, (given the time of year) then spend the whole time based in London. We have visited London at least half a dozen times for a week or so each time. It is only the past couple of times that we started doing day trips. But we limit these to trips taking less than 2 hrs each way by train. Hampton Court, as mentioned, Greenwich for the Royal Observatory and Cutty Sark. Bletchley Park. Windsor. Oxford. Bath. The list is long. As is the list of places within London that you still haven't experienced.

Ten days could easily be spent just in London, and in fact, for folks who get London Passes, getting the 10-day London Pass is about the only way to easily get more than your money’s worth. That’s what we did in 2024, and we had an extended time in London. Still, unless you were committed to strictly London, I’d suggest that a half-and-half approach might give you a more enriching experience.

Five-ish nights in London, then maybe north to York? Or west/southwest to places you and others have mentioned. I’ve never made it to Dover (yet), but if it’s on your list, this would be a great opportunity.

Just wondering, are you an Eagles or Jaguars fan, or is this just the right time to go to London, and that’s who’s playing? For Jacksonville, I imagine the Brits are all calling them the Jag-you-ahhs.

One place that I believe should be better publicized in the tourism press is Greenwich, especially the Royal Observatory. One of the most significant places in England IMO. What one learns there about the history of navigation and timekeeping is incredible. And Hampton Court could also get more props.

For me at least, 10 days is a long time in one place, even London. Why not spend 6 days or so in the capital, then take a train to a smaller place such as Chester, York. Or you could spend a few days in Scotland's capital, Edinburgh.
Travel back to London to be near the airport for the final night.
Bear in mind that October is an Autumn month where the weather might not favour outdoor activities, although you could get a beautiful late summer spell.
Every area will have opportunities for hiking. In the Chester area, you could catch a train for a short trip to Delamere forest or even up to Liverpool/Freshfield for a walk along the beach, dunes and forest.

It seems a shame to be in England and not see something easl apart from London!

There is some super countryside around London - the Cotswolds is the place all Americans think about visiting, but there are other equally as nice (and less busy) places. Kent and Sussex have many small attractive villages as well as a wealth of castles (ruined and still lived in) , cathedrals and small village churches, gardens and lots of walking. There is also the Weald and Downland Museum which is one of the best open air museums with over 50 old buildings which have been rescued and rebuilt here. There is a market place, industrial area with traditional crafts and then the scattered rural buildings, many with thatched roofs and gardens. It really is like a walk back through history.

Alternatively there is Dorset or east Anglia (Suffolk and Norfolk) , which hardly features on the tourist itinerary but well repay visiting.

Cardiff is an easy train ride from London and from Cardiff you can do a day tour by bus to St. Fagan's(outdoor) Museum Welsh Life and on a different day take a train to Caerphilly Castle.

One thing you might want to do while in London is take a tour of Tottenham Hotspurs Stadium. When I took my grandkids (both avid soccer players) to London in late March of 2025, they really wanted to tour a football stadium, so we went to Tottenham, which had just been remodeled.

The stadium was amazing, and they loved the tour. For that matter, I really enjoyed it a lot as well. In addition to everything else, we saw the locker rooms the NFL players use and talked to one of the guys who helps with that. He was telling us some really fascinating stories about players and games. And the staff there were so nice and so helpful. It was really a lot of fun https://www.tottenhamhotspurstadium.com/attractions/stadium-tour

To answer the one question, we are Eagles fans and are going for the game on 10/11.

We prefer to rent AirBNB's so we have a kitchen since we are vegan / whole food, plant-based, and it's easier to stay in one AirBNB the whole time and day trip to and from places so I think we'll likely do that on this trip and pick approx 4 spots outside of London that are convenient for day trips, either by train or on a guided tour.

Be careful booking places on AirBnB. Whilst there are lots of legitimate places there are a number who are more than a bit economical with the truth on location. More concerning is that some letting are illegal, being in social housing on in properties otherwise excluded from short term sub rental. It’s best to check with local experts before committing to a rental.

For a little bit of Philadelphia in London, there are five Passyunk Avenue bar/restaurants, replete with Eagles, Phillies, Sixers, and Flyers banners and jerseys, cheesesteaks, and a game showing on the big-screen. The location on Cleveland Street in Fitzrovia, in the shadow of the BT Tower, would be a welcoming spot before or after the game, or any time during your stay.

The afore-mentioned London Pass includes the Tottenham Hotspurs Stadium Tour, including the changing rooms and The Dare Skywalk rooftop walk. That Pass is the best value if you’re going to otherwise expensive sights, which also include the Tower of London and going to the top of The Shard.