I have the same experience as Mark here in the UK.
It's a tale of bad news / good news here.
The bad news is that our National Health ( free service ) provides little or no therapy for people like us, the therapy they provide is done by 'general' therapists and you can wait a long time to see one
The good news is we have a terrific network of charity organizations that provide rape / abuse counselling or therapy. And like Mark says you pay what you can. I work there now, and I know it costs about $60 per hour absolute minimum to keep the service going. But we generally get very little direct off the client.
The National Health does pay for some who are reffered from a doctor, the rest of the shortfall is made from donations and tireless fundraising.
It's a precarious system, but a good one because it's driven from the bottom by people who are concerned and commited.
All we need is better funding.
The system you describe where you need police records to substantiate your claim is dreadful, and seems solely designed to keep people out of expensive therapy.
Who dreamed that one up - some tight-wad politician I guess ?