Hi, kristie, I agree with the others that the easiest option would be to limit your stay to London and then take a variety of day trips from there (for example, Oxford is definitely doable by day and is a wonderful place to visit!). You could visit Hampton Court Palace, Greenwich, etc. And as others has also said, train travel (or car travel) will eat into your schedule especially considering the time change. Plus the short days will limit your sightseeing.
Or you could stay in London for 3 days and then head for York for the remainder of your stay. Train travel is easiest, I think, although as noted, car travel will get you to more places.
One idea I thought of was that you could stay in London for 3 days, then take the train to York for 2-3 days. After York, you could take the train to Oxford (you would have to do that in 2 stages - one trip to Birmingham, then one to Oxford so you're not routed through London). Even with just one night in Oxford, you could see a lot, and then at the end take the Airline Bus from Oxford, which goes directly to Heathrow for your flight.
It's hard to give advice without more details. What time does your return flight leave? And do you have a full 7 days of travel, or is one of those days included in the flight over?