I don't live in the UK but I sure would hope that if you did not sign a contract, you would not be under any legal obligation to pay her the 120 pounds. If she pursues it, I would call her bluff by turning it around on her. I'd say "game on" -- you will pursue charging her for missing work when she cancelled then. I'd also insist on getting the 10 pounds you already paid back if she pushes this.

I would think if she really tries to back you down, consulting with a lawyer would be quick and easy. Do lawyers offer free consultations in the UK like they do in the USA?