This is unfortunate, you are obviously a really nice guy, trying to help out a custy and it has backfired on you.
I've done exactly the same thing as you in the past and I now think that bearing in mind she's a PIA, I wouldn't touch it without a quote!
Personally, when she sent the message offering £50, I would have politely asked if we could 'meet in the middle', maybe she would have accepted...maybe not.
If not, I would have politely accepted the £50 and dumped her.
Unfortunately, I think you have now dug yourself a bit of a hole (sorry to say that).
Hopefully she will pay you the £50, but if she doesn't you'll have to decide how much hassle you want to go through to recover the £50?
Personally, I actually think it's worth a couple more letters to recover the £50 (only because she has already agreed that £50 was an acceptable price) so technically she has AGREED to pay it.
On a positive note...summer will be here soon, we'll all be in shorts and the ladies skirts will be high.