payment in lieu of notice for extracurricular activity- can they enforce?

[cluttered]

Hi, I would be very grateful if anybody has any legal knowledge about my legal obligations in respect of a demand for payment in lieu of notice. Basically, DS2 has been doing a fairly expensive extracurricular activity for a few years but for several reasons finished in January. I always understood the position was that fees had to be paid at the start of the month before doing any classes for that month and indeed previous invoices have said DC cannot do the activity if fees are in arrears and please let us know if your child is no longer continuing so someone else can have the place.

We have been fairly sure over the last couple of weeks that this would be the last month and finally decided yesterday (January 31st) so I sent an email saying he would not continue in February. They are now saying to me that they require a month's notice so I still owe the February fees. Looking at an invoice sent last week which I had not previously opened it does say that a month's notice is required however no previous invoices do. So my question is, what is my legal position? Do I have to pay this amount of around £200? As far as I know I have never signed a contract. Could they take me to the small claims court if I don't pay?

I'm no legal expert, but it seems fair.
If you didn't notify them until 31st January, how are they supposed to have someone in place and ready to start for February ? Therefore, they are missing out on that income, for those weeks, which needn't have happened if you gave them notice.

I would be happy to pay a lesser amount of notice for example a week but this club is run in quite a loose way and one of the coaches left suddenly with no warning so all the classes have become bigger and I am not sure that they will actually be missing out on income because of DS leaving. It's more that they take as many DC as they can find and squeeze them into the classes so if they have another DC wanting to do the activity they will fit them in regardless of whether DS is there or not.

I have heard from the other parents that the coaches don't give warning when they leave otherwise they don't get paid for their last sessions so the club is a bit tight about money. I am sure if we had said DS was leaving he wouldn't have had much attention paid to him in class. The point is that I had never heard about the month's notice until they emailed me after I said he wouldn't be returning and then it was indeed on the last invoice sent a week ago that I hadn't read but not on earlier invoices. I would feel morally obliged to pay if I had known previously but I didn't. I am just wondering what the legal position is as I don't know whether offering to pay one week's notice means I am accepting liability for the whole amount?