Depends on the scale of your shoot, is it just you and the model? Or do you have a full team?
I have done street shoots in Bristol, sometimes very casual other times fully set up. Not sure about London but Bristol City Council has a department who coordinate shoots in the city, ensuring that there are not two of you in the same place, almost had that once, we were a large team with 4 models and there was a tv crew (Several large campers and trucks) in the next street. Bristol encourages street photography and do not charge for their 'permit ' but insist you have full insurance.
I have found it best to hire a room close to the shoot, many places can hire you a room, hotels being the obvious one, but try pubs and clubs, local community groups, even church halls which can be very cheap.
If you don't want to hire a room many more experienced models will have techniques for changing in pubic without offending anyone's modesty.