(2-part post):
Let's deal with the easy bit first:
I can't see any way in which your son could claim for unfair dismissal in these circumstance but, if you want to check, see here:
http://www.direct.gov.uk/Employment/Employees/ RedundancyAndLeavingYourJob/fs/en
Things now get a bit tricky when it comes to working out the numbers. If I've read your post correctly, your son was with the company for 11+3+1 weeks (=15 weeks) including the disputed holiday period. I'll assume that he worked a 5 day week and that he didn't have a contract giving him more than the statutory minimum holiday allowance. That means that, in a full year, he would be entitled to 20 days paid holiday. So, pro rata, he was actually entitled to 5.77 days paid holiday.
I'll now further assume that this happened fairly recently. If so, there was only one bank holiday during the employment period. My next assumption is that the firm closed on this day but this is the only day of holiday taken by your son (apart from that final week) during his employment. So, in total your son took 6 day's holiday when his actual entitlement was 5.77 days.