I have only ever seen quick trails for this programme so am not sure what style he is wearing exactly but I'd imagine you're asking about the Taqiyah caps. They're available widely in East London if you're that way on, and anywhere with a reasonably large Muslim population you should be able to locate them.
As for wearing one for a gag, well, all I'd say is if that's your dad's sort of humour he's probably best sending someone else to buy one.
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http://www.ebay.co.uk/itm/Burqa-Costume-Burqua-Fancy-Dress-outfit-Traditional-Sharia-burka-bride-/400550799061?pt=Adult_Fancy_Dress_UK&var=&hash=item5d42b026d5
As for wearing one for a gag, well, all I'd say is if that's your dad's sort of humour he's probably best sending someone else to buy one.