Hello josephjpet,
I read your other thread you had posted in January, which basically outlines your time in London and day trips, just as this present thread does.
https://community.ricksteves.com/travel-forum/england/itinerary-in-england-question
You originally said Oxford was important to you.
Oxford and Bath can both be reached by coach (bus) from Heathrow, very easily.
I will throw out the suggestion that you could go to Oxford directly from Heathrow, spend the night, then travel into London. This would give you an afternoon and an evening in Oxford to look around. In your other thread, you mentioned the possibility of seeing Blenheim. You could take an Oxford city bus north (not very far) to see Blenheim.
You would also have the morning that you check out of your hotel to walk around Oxford.
When you arrive in London that day, you would drop your bags at your hotel (too early for check-in) and go see Westminster Abbey and St Paul’s, as planned.
You may instead choose to take the coach (bus) from Heathrow to Bath and spend one night (or two) there.
There's lots to see. Then take the train into London.
Yet another choice is to take a taxi the very short distance from Heathrow to Windsor and spend one night there.
You could tour the castle, walk around the town of Windsor, then head into London on the train the next day.