Welcome the wonderful world of light aviation, and your first lesson. Beware those that look at you as a cash cow!!
Yes this is an very expensive hobby, I once heard it described as more addictive than heroin and twice as expensive!! However, the medical seems very steep. Have a look at the CAA web site, they have a list of all AME's there and call 3 or 4 and find out what they cahrge, expect around 100 - 150 max.
Landings. Sadly as already stated, there are more than one per hour. My first solo cost me £80 in landing fees alone. (£10 per go). USA- yes you can do a JAA licence and the price is lower, but then so is the standard. A lot (Note not all) of the FTO's out there operate a factory production line of students, and you will return with your licence for half the price over here. At least one CFI told me that he would want anyone coming back from the states to have another 10 hours to get them used to flying in our more congested skies. This might be a little over the top, but expect at least another 5 hours tuition before anyone lets you loose in their aircraft!
What you have to do, I found, is spread your wings a little (pardon the pun). For instance, I live 10 mins from Barton. I hate the place, it's culture and the waterlogged grass runway built on a peat bog (dons helmet and awaits incoming) I started at Liverpool and have since moved to Sheffield (for personal reasons). Both are a 45 minute drive away, both have good schools, long tarmac runways and good facilitiles. The best thing about Sheffield is that I do all the circuits I want at another airfield for £10 the lot. This can reduce the cost wholesale, and has for me anyway.
Living in London, have a look around the cambridge / Peterborough area. Yes you have a little travelling to do, but balance that against saving a couple of grand! Then there is the south coast as well, places like Shoreham. Have a day out, drive around these places and see what the commute is like. If you can stand it then book a trial lesson with them, most schools offer these. Have at least 2 (the hours count in your logbook) and compare the equipment, instructor level and price. If you are unsre come back here and ask.
In the flying world we are generally nice people who have a great interest in aviation, we must have as we pay a lot for it, and we will always welcome new members to "our club". If we can help in any way, just ask us!!!