10 nights in England

I think you have two options. One is to stay in London the whole time and do day trips to all the places you mention. The advantage to that is that you can switch it up - a day or two seeing city sites in town mixed in with day trips to the other places. Also can change your plans according to weather. If you get forecasts for some rainy days you can spend them doing museums, etc. in London and use the nicest days for day trips. The down side of course is you spend some day backtracking, Bath especially is about 2 hours each way so longer on trains. You also don't get to experience another place in the evening - although in June it won't be dark till about 10pm. The other option is as you say, move lodging halfway through the trip and stay in Oxford or somewhere else. The cotswolds is the only place that will be difficult without a car. There are organized day group trips you can take from London but to really enjoy the area you need a car. But if you've never driven on the 'wrong' side of the road there is a learning curve to it and I'm not sure it's worth it just for a day or two. When I've rented cars in the UK it's been because I was visiting areas for a week or two that required a car. You certainly don't need one for Oxford or Bath themselves. And if you do decide to rent one I'd take the train to Oxford or where ever and rent the car there, not in London.

There are small-group tours of the Cotswolds originating in both Bath (MadMax and possibly others) and Moreton-in-Marsh (GoCotswolds and SecretCottage). Moreton is a short train ride from Oxford. I wouldn't want to take a bus tour all the way from London, because there would be an awful lot of sitting-on-the-bus time. I also wouldn't like any tour of that area that uses full-size buses; they're too slow to load and unload at each stop. A car would be the best way to enjoy the Cotswolds, though I was perfectly happy with my GoCotswolds tour.

To me, the comparatively high cost of lodgings in London is a significant deterrent to doing a lot of day-trips from that city. However, lodging in Bath, Oxford and Cambridge isn't exactly cheap. With a rental car you wouldn't have to be tied to staying in one of those higher-cost towns, but then you'd have parking challenges upon arrival for sightseeing.

Although I'm a huge fan of having a flexible itinerary, you have to be careful about buying last-minute train tickets in the UK. For some destinations that can be shockingly expensive. So I'd definitely check the cost of Anytime, Off-Peak and Day-Return tickets to my potential destinations on the nationalrail.co.uk website to see whether there are any that are only affordable via purchase of cheaper Advance tickets. Advance tickets often need to be purchased quite early.

Based on posts on this forum, Harry Potter World sells out far in advance. Tickets are currently available for June, but buying those tickets is not something you should postpone until April or May. Definitely the day at HPW has to be pinned down way in advance. The website has good information on how to get to the studios. If you want to visit the studios without a car while you're staying outside London, it would be very important to map out the train journey from your non-London base to Watford Junction on the nationalrail.co.uk website.

Given what you want to see, I agree that moving out of London makes sense for your second 5 days. I'm going to recommend you base yourself in a Cotswold village like Stow-on-the-Wold.

Daytrips from London waste too much time sitting in trains. The other areas you have in mind are all in an area northwest of London and you would be repeating the same train trip day after day.

Just getting out of London is nice. You'll see different villages and shops and pubs.

Once out of London, driving is much easier and much more convenient if you are doing a lot of day tripping. Trains will get you to cities, but not to villages or anywhere interesting in the Cotswolds, for example.

The places you have in mind (Oxford, Bath, Stratford, Cotswolds) are all in a circle around the Cotswolds. Stratford is 40 minutes from Stow-on-the-Wold; Bath a bit further at 1.5 hrs.

I would take a train from London to Bath, see the sights of Bath, rent a car, and drive to a B&B or inn in the Cotswolds. Then day trip from there to your other destinations. You should be able to drop your car off at Oxford and train back to London from there.

Fantastic trip you have lined up. Enjoy!

Since you are flying out of London, I would reverse the order of the trip. After arriving at Heathrow, take the National Express bus to Bath. Spend a night or two there, then pick up a rental car and head to the Cotswolds. Spend two to three nights there, with a day trip to Stratford. On the last day, drop the rental car off in Oxford. Spend the day exploring Oxford, and take an evening train to London. Spend the remaining time in London, with a day trip to Harry Potter World.

Five days to do Oxford, the Cotswolds (need two days), Stratford Upon Avon (yes, it's great) and Bath (2 nights). You are one day short. Yes, you can only do one day in the Cotswolds, but we did it in two. Don't miss Cirencester. Do Oxford and then rent a car. You don't want to rent a car and have to deal with it while in Oxford. Very little parking.
Consider staying two nights in Bath, at the Brooks Guest House, also dine at The Scallop Shell (best Fish and chips ever).

Your children will probably be bored rigid by the Cotswolds. Head from Heathrow to Bath for 2-3 nights, as day 1 will be lost to jet lag. Move to Oxford for 2-3 nights and cover Stratford-upon-Avon from here as a day trip (be warned SuA is full of tacky tourist shops and to me, a great disappointment).

Do Harry Potter from London - easy by train from London Euston.

I would opt for Oxford or Cambridge, otherwise you aren’t going to have long to see London itself.

Thank you everyone for your help! As always it's so helpful!
Because we found a rental in London that will work so well for us and it's only available June 8-13th, we will start in London and finish our trip in Oxford. We also found a great place in Oxfordshire!

England was our oldest daughter's choice because she wants to visit Cambridge and Oxford so I think we are going to visit both universities. I know visiting Cambridge will limit our time in London but we will have to deal with it.

So here's the itinerary:
June 8: A.M. arrival. Check in and rest.
June 9: London
June 10: London
June 11: London
June 12: Day trip to Cambridge (or on any of the days above)
June 13: Check out and head to Oxford

June 14: The Costwolds private tour - thanks for the suggestions! I will book one soon.
June 15: Oxford
June 16: Stratford
June 17: Free day!
Jun 18: Fly home! Any suggestions on EASIEST way to the airport from Oxford? We are ok spending $ for convenience.

Unfortunately, we will have to drop Bath for now but another child would really like to visit Windsor Castle.
Any suggestions how we can fit that into our schedule?
Do you think we can do that on our way to Oxford? (but we will have our luggage with us)
Should we rent a car from London, drive to Windsor and return the car at Oxford? My husband is very comfortable driving on the other side of the road.
With Royal Ascot taking place, do you think it will be overly crowded and not worth our visit?
Advice please!

We really enjoy medium paced ;) vacations so I don't want to overdo anything, so feel free to suggest!
Thanks again.
Grace

That’s a lot of day trips without thinking about Windsor, especially at the latter part of your trip. How much input did you get from the teens? You don’t want a civil war breaking out. All that time in transit can lead to bickering and sniping if everyone isn’t 100% on board.

Are both universities an absolute must?

I’d also get 100% buy in on the Cotswolds. You know your family, but I could see younger teens being bored to tears.