Oh, littlestar, I sympathise in a big way. I went through this very same trauma. But, I started causing a stink when I was about 6 weeks pregnant. I am in the catchment area for St. Peters in Chertsey. I went to my GP (in Sunbury, which is where I live) and told my gp that i didn@t want to got to St. Peters. He said "I'm afraid you don't have a choice." and went on to tell me how it was Blair's fault for telling people they have a choice when in fact they don't. Well, to make a really long story really short, I up and changed GPs to one in Hampton (who is lovely lovely lovely compared to the wanker doc. in Sunbury). She tried to get me into Kingston, and failed. She tried to get me into West Middlesex, and failed there too. So, she asked for my next choice. We tried for Queen Charlotte and Chelsea in HAmmersmith. They accepted me, and I am delighted with the prospect of going there.
Is this your first baby? Why are you unhappy with the current hospital? Do you know how you want to have this baby (vaginally, drug free, epidural, birthing pool, homebirth, caesarean, etc.)
I am now 22 weeks pregnant. My first was born by emergency caesarean at Epsom General (lived in Epsom then). So, I want an elective caesarean this time. One of the reason's I wanted to go to QC and C is that they are fairly agreeable to caesareans if you push for it. They won't be the first to suggest it, but if you really want one, they will book you in to see the consultant at 36 weeks, and if they still can't change your mind, you can have one.