If they were placed end-to-end, how many average-sized enchiladas would it take to encircle the UK?

SHORT ANSWER 

69,904,183

FULL STORY

The UK coastline measures 7,723 miles which is the equivalent to 13,592,480 yards or 489,329,280 inches.

A standard tortilla wrap has a diameter of seven inches and therefore when rolled up it would also be 7 inches long.

The number of enchiladas required is therefore found by dividing the two which results in a mere 69,904,183 being required.  After taking the time to lay them out end to end you would be forgiven for eating the one-inch overlap that will result.