I would advise you to exchange pocket money from Doha (Souq waqif has some of them and banks do too) and use ATMs once you get in UK..

If you use underground tubes from Heathrow, be careful because there are professional thives who will stop you saying they lost thier wallet and they need some money so try to avoid those- better if you go with someone.

Whenever I am in rush, I explain this to clerks in visa section, they are always accomodating those requests but let them know your request is urgent to some extent.

I believe weather should be cool by now.