Priceline
Aine,
I've used Priceline a few times to stay in London and generally have been quite happy the price I've paid.
A few pointers-
You will have to use a valid UK post code on your home address. Also a UK style tel no. I've use my Irish address with the UK codes in the past and it's accepted by the system. Technically your probably breaching their T&Cs but it works.
I've used an AMEX to book rooms. Don't remember if it will accept non UK Visa, MasterCard, etc.
Sometime hotel chains have special offers that could offer better value than priceline. Have a look at
www.thistle.co.uk who have a large number of hotels in London. Most (except London Ryan) are quite nice.
www.biddingfortravel.com and have listings of hotels that people have been successful with in each zone. These sites also have some good FAQ on bidding strategy. First site generally refers to priceline.com while second is for .co.uk
Occasionally I've felt that the rooms (while adequate) were a bit on the shabby side. If I was paying full price would have been very disappointed. There are some discussions on above sites about this. I'd almost stick to 4*.
It's important to have an idea of the prices being changed in each zone so you don't overbid. The hotel listings at the above links will allow you do some research so you don't overpay. In the past I've started bidding at about 50% of the lowest rate available and increasing from there.
Don't set your heart on a particular hotel as it is a lottery.
John