QUOTE(lorraineliyanage @ Jul 13 2012, 08:54 AM)

Definitely sounds like a scam but you said there was a recommendation so I am not sure. Who is the parent that recommended them to you? Did they give the name of the parent? If so, it's less likely to be a scam.
Just don't hand over any bank details or accept a cheque for an overpayment of lessons. I would seal the deal with cash payment only at the door as miff says if it's a scam!
Thanks for all the replies - although they have worried me a bit!!
I did actually think - at the beginning - that it might be a scam, but they gave the name of the people who had recommended me. Both fathers are doctors at the local hospital (the one who contacted me yesterday presumably doing some sort of temporary consultancy), so that sounds plausible enough. I phoned him back, and we made an arrangement for a lesson at the beginning of August. I then confirmed the arrangements by email, adding that payment would be cash or cheque at the lesson.
He seemed quite happy with that, but I WILL proceed with caution, because he seemed quite keen for me to take the girl for an hour (post Grade 1 standard). The daughter is 17, so it's likely that she would be okay with an hour, but I told him that it was probably better for a first lesson to do just half an hour. Assuming that they do turn up on the appointed day, I will push for cash, but if they pay by cheque I will bank it straight away, so if it all falls apart and the cheque bounces, it's only going to be a modest amount for a half-hour lesson. I can then cancel any other arrangements made, and I certainly won't accept bank transfer or a cheque made out in error for too large an amount.
I'm inclined to think it's genuine. He gave me his mobile number, and also the number of the local hospital where he is currently working. He also gave the name of his secretary there, so I suppose I could actually check this out. I had an email back from him this morning to say thanks and he hoped his daughter would enjoy her lessons, so for now will wait and see what happens next.
I hope I am not being too trusting.....but will keep you posted!