To continue on with what I said above.......
It is very easy to get on a bus at one of the bus stations within Heathrow Airport.
You could go to many places directly from Heathrow and leave London for later in the trip.
That's what I'd do!
And I've been to England and to London many times.
My advice is to save London for later in your trip, when it's not as crowded.
Back to the subject of the bus......
We landed at Heathrow (early in the morning) a couple of years ago, and took the bus (coach) from there to Bath.
You can just follow the signs in Heathrow that point down the hall, saying "Bus /Coach Station".
Walk up to the window with the attendant to buy your ticket.......to just about anywhere.
(Bus tickets are CHEAP compared to the train; at walk-up prices, especially.)
We bought our tickets to Bath, boarded the bus, and were there in about 2 hours.
The bus has comfy seats, WiFi, and when we traveled there were only two other travelers on the bus.
We arrived in Bath. The bus and train station are in the same location.
We walked to our hotel and were there in time to drop our bags and head out for lunch.
You could spend several nights in Bath.
It's a great place to walk around and see the lovely architecture.
Great shopping too! Lovely clothing stores. Lots of cafes and good restaurants.
On the second day, you could head out on one of the Mad Max Tours mentioned already by others.
(They're very popular here on the Forum.)
Have a look: https://www.madmaxtours.co.uk/
After 2 to 3 nights in Bath, you can take the train to another destination.
OR.....You could choose many other destinations when taking the bus from Heathrow.
You could go to Oxford, and stay there a couple of days.
Then onward to the Cotswolds, which are a short distance from Oxford.
You could take the train from Oxford to Stratford-Upon-Avon for a couple of days.
You could take the "Go Cotswolds" tour from Stratford-Upon-Avon on one of the days you are there.
We have taken this tour more than once and love it!
Take a look. You want the "Cotswolds In A Day" tour:
https://www.gocotswolds.co.uk/tours/
They pick up from locations other than Stratford-Upon-Avon, too.
In short, I myself would stay clear of London during the crowded Bank Holiday Weekend and Queen's Celebration.
You could make out a schedule in which you put London in the middle of your time in England.
From London, you could catch the train north to York and spend several days there.
I would be changing your London hotel reservation immediately, if you wish to escape the Bank Holiday Weekend and Queen's Celebration crowds.
I hope this is helpful.