Gary, If he works part time for you Wed - Fri, does he work for anyone else on Mon and Tues? If he does remember he will get some entitlements from them too!
If he has signed a contract as per what you have set out, then he must have been happy with those terms (or not read them properly!) From what you say he isn't entitled to hol pay from you ar all the xmas week. It sounds tough, but you are running a business and if you do something out of the ordinary for one, then you will start the ball rolling with others wanting the same and more! Personally I would stick to the terms of his contract, but maybe issue an Xmas bonus to all staff, pro rata of course! It is a tough time of year (xmas) to be making decisions, but last year we had to sack one 3 weeks before xmas, personally, we felt terrible about it, but it was the right business decision to make. Just one thing, are you taking the whole of the xmas period off as a business? If so, if he has enough accrued holiday he will get Wed to Fri paid anyway! and surelt that is what he is used to the rest of the year!