London Trip

Sue, of course it is possible, is it advisable might be the better question. Many here will say no,, you will only get the briefest taste of each place, but, I have seen many posts on tripadvisor.com where people literally have 10-12 hour layovers at the airport in Paris and will dash into city for a quick look around! So , with 6 days , yes, you could see a tad of each place. Fly into London, spend first day there, see British Museum and Tower of London, then second day, perhaps Imperial War Museum , Buckingham Palace( just outside) Victoria and Albert museum,, or for a quick peek at quite a few places, get a two day pass for a HOHO bus.. you can jump on and off at the sites that interest you personally. Third day, go to Bath, I like Bath, many will say don't leave city with only a few days , but I think it was worth it,, its personal tastes. Now, this is "hump day" you could take the Eurostar to Paris later in day, arrive for late dinner, take a night cruise on the Seine, or just wander about. Next two days to enjoy Paris, you could see a fair bit, be sure to time trip so things you absolutely must see are open on days you are there, many museums close on monday or tuesdays. Last day , fly out of Paris. The Eurostar is 2 hours and 35 minutes. Second class if fine, take some of your own snacks on board. Its convenient as its city center to city center. If you book your tickets as far in advance as possible you will get best prices . Sue, I personally would hesitate to do all this, but I understand some people don't mind moving around and seeing a bit of a lot of things, as opposed to alot each . So go with your gut .

it's possible but not recommended
7 days barely covers London OR Paris

While it may be physically possible, with 7 days I would not waste my own precious time in Bath. A very nice town, yes, but nothing near the experience of London or Paris where you could spend 7 days in one city and still not see everything you want. Spend 3/4 or 4/3 in London/Paris, or better yet try to squeeze an 8th day into your plans and spend 4 full days in both places.

The biggest deflector for me in doing this would be the added cost of the Eurostar (though the experience would be cool). The air fare may be comparable, but the train ride would cost between $130-$200 for coach (depending upon your needs and when you book). That is another night in a hotel. And quite a bit more than the $40 for a ticket to Bath. But obviously it is worth it for many or it wouldn't exist. Clearly both cities are worth seeing. If you never plan to go to Europe again, then ~$150 per ticket could be worth it. If you plan to return, maybe its worth saving Paris for its own trip....

Gary, the cost for Eurostar can be as cheap as 50 euros ,, if one buys in advance prices an be very reasonable. In fact go on the Eurostar site, look at prices for 90 days out, you may be surprised, don't go on RailEurope site though, they tend to charge more!