Doing things for free is fine for to start I think.
I would never consider charging a measly amount of £10-£15, it's more hassle than it's worth and the client wont value you anywhere near as much.
Personally, designing for free does me fine at the moment, as I cannot make any guarentee's about the final product. Once I've got in my groove as it were then I can be confident in exactly what I'm offering and prices and such. Of course if you're already confident in what you do, definitely charge a reasonable sum, although as Pixels says expect to lower your prices a little to start with.
Also, I agree that haggling an offer of £20 down is a major insult, I would consider anyone haggling down anything under £50 for an unproven designer insulting. Get real fardeen.