London base or move around?

It all depends on you. I'd want a change during a 10 day trip; others would love being based in London the whole time.

For Bath, an advantage of staying there 1-2 nights is being able to see things before and after the daytrippers do, as well as being able to see more than on a daytrip. For the Cotswolds, it depends on what you want - just to taste them, or to have more of an experience being in them?

There is no right or wrong answer - it all depends on your personal preferences, and your goals for the trip.

I would move.... Your lodging would probably cost more in London so why not find a cheaper place to stay plus be closer to where you want to visit so you have more time on the ground than in transit?

Thank you! It's a good point—I definitely prefer to immerse myself in a place rather than simply get a taste (it's why I don't enjoy cruising). I want to experience as much as possible while there ... never been before and I'm a huge Anglophile.

If the trip is 8 days, I'd be inclined to stay in one place. You lose time checking in and out of hotels, there's the remote possibility that something gets messed up with a reservation, and with 3 separate hotels that can increase the chance that something is wrong with a room and you'll have to spend time correcting it. The advantage of having every night in London is that even if you get hit with rain, there's a lot more to do at night that there would be in the Cotswolds or even Bath.

I'm not a big fan of Bath for aesthetic reasons (I found the uniform Georgian architecture dull), but I think you can base there and get a tour into the Cotswolds. You can also tour the Cotswolds from an Oxford base by hopping onto a train to Moreton-in-Marsh. Oxford's hotel rates are probably lower than Bath's.

Having done one day-trip to the Cotswolds hardly makes me an expert, but I think unless you want to hike from town to town, you don't need a great deal of time to get a sense of the area. The towns are mostly small; they don't need even 1/2 day each. An hour or two will do unless you plan a full restaurant meal in one of them. A tour that moves from town to town will give you a decent view of the countryside. A combination of one day for a day-trip and one day to do some walking (if the weather cooperates) might be a nice middle-of-the-road combination. Rick describes some town-to-town walks in his guide book to Great Britain. Moreton-in-Marsh seems to be the transportation hub for the Cotswolds. You could stay there for both a tour day and a walking day.

I think touring the Cotswolds from London, while possible, would pretty seriously cut into your time actually in the Cotswolds.

There is so much going on in London: many huge museums, the theatre, the markets, the other sights. I would find it hard to tear myself away for a day-trip anywhere. As already pointed out, the hotel costs run high, so using a London-based day to visit a town where I could have stayed for a much lower price would have felt sort of extravagant to me, though I do really dislike one-night stays.

For eight nights I would pick two bases: perhaps five nights in London and three elsewhere. I spent eleven nights in London last month and it wasn't enough, but my travel pace was very slow.

I think acraven had a good idea (even though he doesn't like Bath) -- start with 2-3 nights in Bath, including a day tour of the Cotswolds, then train to London for the rest of your time. Mad Max offers a one-day Cotswold tour that looks good; I haven't taken it but the company has a good reputation. You can get to Bath relatively easily from Heathrow, and to London quite easily from Bath.

Alternatively, I'd suggest staying in London the whole time, with one or two day trips to nearby places that might interest you like Greenwich, Hampton Court, Windsor, Cambridge or Oxford (not both), etc.

One thing we've discovered that works best for us on vacation is that, save for an airport hotel the night before going home, we're happiest if we have three nights in each location rather than jumping around too much. It lets us explore more in depth and you aren't losing the fun time by finding the hotel, checking in and out, cramming everything back into the suitcase, etc.

We had a longer trip this year than you're thinking and it got mapped out as:

First three nights: Salisbury-Stonehenge area- not an insane drive from LHR and a little quieter so we can more gently get over jet lag.

Next three nights- Swansea (had equivalent of 240 euros in hotel vouchers by doing the Club Opinions surveys program for Le Club Accor) let us see Tenby and Brecon Beacons NP. Generic business hotel, but hey, it was zero out of pocket.

Next 3 nights- Snowdonia National Park area. Hiking, Portmeirion, lots of sheep sightings.

6 nights in London- in which I blow basically all my Holiday inn points stash for a reward stay at a apartments-style Staybridge Suites that is breakfast included, has nicely functional kitchens in each suite, and has a self-serve laundry to get rid of the Welsh countryside dust. I know when we're traveling we often reach a point when we'd really just rather grab a quick and easy dinner from a takeaway or the prepared foods area of a Marks & Spencer grocery store instead of dealing with a restaurant again, and the kitchen helps make that easier.

If you both have good credit and somewhat flexible vacation at work, the major airlines will typically have credit card promotional offer out there that will get you the 60K airline miles for a 'saver level' European award ticket that will cost you somewhere around $150-$200 in UK airport departure taxes out of pocket (just avoid redeeming on American's alliance partner BA if you go the American route because they have high award ticket surcharges). Then take the money saved on plane tickets and add days to the trip or upgrade your activities or dining plans instead.

I recommend the following company for touring the Cotswolds:
https://www.gocotswolds.co.uk/
"Go Cotswolds" picks up in Moreton-In-Marsh. You could take the train from London to Moreton-In-Marsh, check into a B&B and take the Go Cotswolds tour the next morning. Then stay in Moreton one more night, then train back to London.

We took their tour last spring. We were staying in Stratford-Upon-Avon.
We went to Chipping Campden, Broadway Tower, Stow-On-The-Wold, Bourton-On-The-Water, and the Rollright Stones, to name a few of the stops. Tom gave out walking maps in some of the towns, and made recommendations for shops selling coffee and cakes, or lunch. Plenty of time was given for us to walk around and take photos at each stop. We highly recommend this company.

Here's my trip report with more information:
https://community.ricksteves.com/travel-forum/day-tours/go-cotswolds-tour-with-tom-the-most-fun-we-had-while-in-england

There are so many places that would be good for a short trip from London. Bath has been mentioned, but you could also go to Oxford, Cambridge or York.
Here is a company that leaves from London for the Cotswolds:http://www.walks.com/other-tours/day-trips-from-london/
With the London Walks company, be sure to check their website for which days they go to the Cotswolds.

I've taken the Cotswolds tour offered by MadMax out of Bath. Mine was given by a part time guide who grew up and still lives in the area. HIs full time job is a stone mason so he was able to add a lot about the buildings all over the area. He even explained what goes on when one of the older houses is renovated.

You go to Castle Combe, Upper and Lower Slaughter, Stow on the Wold (lunch stop), Bibury, Badminton and Tetbury. (You will drive through others.)

The tour is in a van that holds 15 people.

Madmax gives other tours that include Stonehenge and Avebury.

You could also look at London Walks. Not only do they offer numerous walking tours in London but depending on when you go offer day trips out as well.

I would count your time by the nights you will be there. Two nights equals one full day, etc. Having been to all the places you mention, I would say not to short change London. When we flew into Heathrow we rented a car and drove to the Cotswolds. We spent 3 nights in Chipping Campden, so had 2 full days there. We were fortunate that someone who grew up there drove us around for the 2 days. We would have seen a fraction of what we did on our own. Thanks N! We spent 6 nights in London (2nd time there, and did a day trip to Bath from London. We took an early train there and a late train back. While there we toured the Baths and the surrounding area ourselves, then took a walking tour. I felt we saw quite a bit. If you have 9-10 nights I would suggest going to Bath upon your arrival, staying 3 nights. That would give you a full day in Bath and a day to do a Cotswolds tour. Spend the rest of the time in London. If you only have 8 nights I would probably either spend 2 nights in Bath (Cotswolds tour on your full day) and the rest in London. If only 7 nights just stay in London and do a day trip to Bath. Save the Cotswolds for another time. If you find a great air/hotel deal then just do day trips from London. Last year we did an air/hotel deal to Paris for a week. It was the first time we've ever gone to just one place. We paid for the package what the regular price of what the airline tickets would have been (I checked those exact flights), so we got 7 nights in the hotel essentially for free. Great deal!

Whatever you choose you will have a great time. Happy Anniversary!