London/Bath 5 1/2 days for both

I think the starting in Bath thing only applies if you are doing a longer, round Britain trip. How much do you want to see Bath? It sounds like you'd rather spend the time in London. You can take the train from Gatwick to Bath, but it takes over two hours and you have to change in Reading.

We flew into Gatwick, picked up car and drove straight to Bath. Can't remember how long it took. We don't seem to suffer from jet lag so it was fairly easy for us. We stayed two days in Bath and made day trips to Wells, Stonehenge, Wales and then headed back to Windsor. Half day there and then went to Horley, little town outside Gatwick and we took train into London for two day trips and then back home from Gatwick. A lot depends on what is important for you to see and if you have a car and also if you need to decompress from your first day arrival. If you do stay in Horley the night before departure, many of the B&B's will provide free transport to airport. Also try to eat at the Six Bells restaurant, about 400 or so years old. Enjoy.

I wouldn't. We like to base ourselves in London for stays similar to the length of yours. We have done Bath as a day trip (by train it's very easy) several times. There are lots of other day trips to do by train, too (several of which I prefer over Bath, if I have to rank them). York is great, so is Cardiff. Stratford-upon-Avon, Canterbury, Dover, Brighton, Winchester, and many others are also very good. With only 5 days, I'd do Windsor (full or 1/2 day- great for when you have theatre tickets in the evening), and maybe one other.
This article I wrote a few years ago might be helpful http://www.aaacarolinas.com/Magazine/2008/Jan-Feb/britain.htm?zip=28105&stateprov=nc&city=matthews (I wrote this after more than 40 trips in just over 20 years- feel free to pm me if I can be of help)

I wouldn't try going to Bath first since you only have a short time. If you want to see Bath you could do a day trip. But there is so much to see and do in London that you might not want to give up a day since this is your first trip to London.

First time in England, only five and a half days. Spend all those days in London- there is so much to see that you wont do half of what you want. While you are there, you could decide to do a day trip just for a change: Howver- Windsor, hampton Court, Salisbury/Stonehenge/Avebury; Canterbury; all rank above Bath in my opinion, and are easy to get to from London. Keep Bath on your list as a possible- but i wouldnt be surprised if you dont get there- it is a long way from London. Takes at least a long tiring day to get there and back no need to commit to it until you are there

Agree with Brian, with one exception. Bath is not quite two hours by train from London. Start early and come back after dinner and you can have a nice, full day in the place. I've done it a couple of time and it hasn't been anymore tiring than spending a day in London. Ticket prices on the day of travel aren't that outrageous, so why not leave it open ended?

Thanks to all who replied; it confirmed our decision to base in London and day trip if the spirit moves us - Windsor is a probable.