I am actually going to Fischer for my top surgery really soon. The stuff in the link that Farm Boy posted is accurate except for the price, which has gone up since then. My surgery costs $7300 (not peri, but I think she charges the same for both) plus $100 for the consult the day before surgery. Also, you have to get bloodwork and a physical done, plus you will get a prescription for pills that you will need to get filled, which also can cost quite a bit if you pay out of pocket.
Ideally she wants you to stick around for about a week to ten days after your surgery for drain removal, but that is not always feasible for everybody. You can have a surgeon back at home do it, but since you will be coming from the UK, it would be better that you get them removed by Dr. Fischer herself. You will probably be allowed to fly after surgery, but it will probably suck a lot, especially with the drains since they will be a hassle with security and you would have to get up during the flight to drain them a couple of times. So by my estimates, if you fly in the day before the consult (she does them in the morning so you will want to be there the day before so you will not be late), have your surgery the next morning, and get the drains removed 10 days later (the longest of the estimated time for drains) then fly home the same day, you would be spending 13 days and 12 nights in the area.