You should check out Gluten-Free UAE. They are a great resource about all things gluten-free in the UAE and have a lot of information about Dubai.
When you are in London, look for groceries in Tesco and Marks & Spencers. They both have their own gluten-free food line. In London, they call gluten-free "Free From" foods. Be sure to look for those.
Gluten-Free Mrs D is a London-based blogger who has a lot of information.
Just check that it says free from gluten. I think 99% of products in free from ranges are gluten-free but I have on occasion seen something Free from that might just be dairy and soy freee for example.
If you find yourself in Brixton Market, check out the gluten-free cafe. I wouldn't make a trip there speciifically to go to the bakery though. The food is great but they cook it all fresh so go to early and there won't be much choice.
Marks and Spencers are good- they have their own small gluten-free range but they also note on packaging of some of their regular ranges if it is gluten free.
I went to Borough Market a day that only half of it was open, but there were stalls that did gluten-free.
Lots of cafes in England do jacket potatoes and you can pick the fillings. Not always ideal but a potato with some tomato and onion and cheese is better than nothing. Obviously just check that they haven't done anything strange to the potato- like coating it in flour.