Cat, I'd stay away from travelodges and premier Inns...as previously said, a lot of premier inns use keycards to get in the lobby alone, and travelodges are pretty divey. If you want to use hotels, you really need to speculate to accumulate, which is a bugger if you don't have concrete bookings as they start at ?100 per night if you're lucky.
Try and see if you can rent a room in a flat for a couple of days instead. It'll be a lot more private, and convenient. There's already a couple of ads in the seeking/offering section I'd try out if I was you - it'll leave a much better impression with the client and will be a lot more safer and comfortable for you, and might be a lot cheaper than getting a half decent hotel in London.
The last time I tried a Premier Inn, I had to give clients the keycard through the window so they could come through the lobby discretely, and the wall were so thin I dread to think what the rest of the inhabitants heard! As for the creaky bed...oi vey! They ?29 ones are cheap for a reason...