I've used Priceline everywhere, including London. I just need to warn you that rooms in London and most of Europe are for only 2 people, one time I stayed at a Sheraton by Heathrow airport and was given 2 twin beds! It has saved us big bucks and I continue to use it, but you need to understand the limitations. Do not expect cribs or rollaway beds. They say 2 people and you may have to deal with it. That said I have had my daughter sleep in a double bed with us before or bring a bouncy chair to sleep in and no one complained.
It is non refundable, non changeable. I would look on bidding for travel to get a better explanation. They have decent lists that tell you what properties have come up in different zones with different star levels so you have some ideas.
You put in your date requested, zone requested and price you offer and then it tells you if you get it or not. If you get it, your card is automatically charged, no chance for changing. If not, you can rebid in 24 hours or you can change your bid slightly. ex. you bid for a 4 star hotel in zone A, you don't get it. then you should raise your bid slightly and add another zone like B that doens't have any 4 star hotels so in essence you are just raising your bid. Read all the info before you bid.
I find that I can almost always get a better hotel than I planned at a cheaper price by using Priceline, but you need to know what you are doing. For your first experience you might find it helpful to have someone who has experience do it with you or try it and go all the way until you give a credit card number just to see the steps and think about it.
Jenn