I love parodies too... would have trouble picking just one (will have to think about it).
But -- will post this now, because the link will only be active for another day or so -- til 11.30 a.m. Tuesday 13th April (British Summer Time). Here is a link (in the second column from the left -- titled "Listen to the Latest Programmes", sixth one down) to "Follow That with Your Sea Lions!" a recent BBC radio programme on comedy in British Folk Clubs; you can hear Fred Wedlock singing "The Folker" as well as Jasper Carrot, Max Boyce, Billy Connolly and (dare I mention his name?) Mike Harding... and more.
After 11.30 on Tues, if you click on the same link you will get part 2 of the same programme, which will be available for a week. (After 20th April, it will be a different programme again, but prolly on a completely different subject -- I don't know what, 'cos I don't have the Radio Times for that week yet.)