To keep track of the payments streamline should send a statement of receipts made.
As for keeping track of them, it is dependant on wether the membership is just a rolling membership or are they tied into a contract for so long, if they are tied in then you will need to keep track of them so as if they have not paid membership you can chase them up as they would be in breach of the contract, if it is not tied in then this will just be classed as revenue and you will to need the details, also there could be potentially be an issue with the Data Protection Act.
If an annual membership has been paid then you will need to account for it on a prepayment basis as some of the money you receive will not be related to the current tax year, so you will not need to be taxed on it until the following year.