Someone may be around soon who knows far more than me, but I can't imagine CFA (no win no fee) arrangements would work for most victims for a few reasons:
-even on a CFA basis, you are going to be paying the other side's cost if you lose. A rape case is never going to be straightforward so this is going to be at least five figures. Even if your lawyer tells you you have a good case, it's still a hell of a risk.
-the amount of money a solicitor can charge in a CFA case is limited to a set proportion of the damages, i think it's 25%. Against that background, I expect CFA only 'works' for solicitors money-wise if they can achieve a quick out of court settlement. But that's going to be rare in rape cases - it requires the rapist to admit liability/guilt. So you're basically going to trial in most instances, and I expect that most competent solicitors wouldn't be prepared to do that in exchange for a small proportion of the likely damages.
-also, bear in mind that, no win no fee or otherwise, if the claim fails, that creates a pretty open-and-shut claim for defamation in respect of a false rape claim.
Otherwise put, the criminal and civil law in this area is, in practice, almost uniquely fucked. I recognise that tinkering with the standard of proof could be a slippery slope, but I also think there could be scope to distinguish rape from many other crimes in this respect.