Day trip/tour to Liverpool from London

2 full day trips/tours (1) combining the Cotswolds, Stonehedge, Bath and Stratford on Avon.

That is much too much for a day trip, even if you weren't coming from London.
Cotswold's = 1+ days. It would be a long day trip. You would need a car or a bus tour.
StoneheNge is usually combined with Salisbury, as that is the nearest station.
Bath needs a full day.
Stratford upon Avon is in a different direction, no way to combine with any of the others.

(2) Leeds Castle, Dover - This pair is doable in one day.

Liverpool would be a long way for a day trip.2½ hours by train.

Some commercial tours do somehow manage to combine up to Stonehenge, Cotswolds, Bath and Oxford, but in an increasingly meaningless way the additional number of destinations are added.

You could do Liverpool in a day but would have to leave London at round 0630 arriving in Liverpool around 0900 and get a late train back to London, this could be a very long day but worth it, if you do this make sure to book train tickets in advance 3 months is normally the earliest to get the best fare as buying on the day can cost around £200 pound return per person.

Jay

I had found a full day 12 hour tour with greyline that included Bath, Cotswolds, Stratford on Avon and finally Stonehedge. Too much? We generally do tours when visiting destinations to experience the most.

And do they say how much time the tour spends in each place? From my rough estimate, it will take at least 8 hours of driving just to get to and from all of those places, which leaves you a whole hour to see each one.

I think the only thing you'd see on a tour like that is a lot of traffic, BTW it's Stonehenge (no hedges involved).

A cousin of mine is a major Beatles fan. A number of years ago he went to London with his family. He wanted to go to Liverpool to take a Beatles tour. They didn't. So he decided to do a day trip up to Liverpool while everyone else did their own thing in Europe.

The train was delayed and he missed his tour.

However, in London, there are a few Beatles oriented walks: London Walks. Just do a Beatles search.

If you go to Liverpool, allow a full day to appreciate the Beatles heritage. Magical Mystery Tour bus takes about 2.5 hours and your bus ticket gets you free entry to the reconstructed Cavern Club. Beatles Experience museum at the Albert Dock could take a couple of hours to savor the exhibits, not counting a possible wait to buy entry ticket if there are many people queued ahead of you. Have lunch or afternoon tea in the Hard Day's Night Hotel, which has an 'Any Time At All' menu.

If you had more time in Liverpool you could also book the house tours that go inside a couple of the Beatles' boyhood homes, but it doesn't sound like you'll have time for that. As a 'Day Tripper' from London I'd say buy your 'Ticket to Ride' and arrive 'The Night Before', sleep in Liverpool and then start your sightseeing in the morning.

On the whole, your list of desired destinations is more realistic for 2-3 weeks, not 7-8 nights.

As a big Beatles fan who's been to Liverpool 3 times on trips spanning 20 years, watching the Beatle tourism options expanding over that time, I'd tell you that the tour where you go inside John and Paul's childhood homes was the most memorable thing of any of those trips. You have to book in advance, limited number of people can go per day.

If you can get a train that allows you to arrive in time to do it then great, if not, I'd follow the rec that you stay one night there to make sure you can!