I'd suspect the longest continaul service of any aircraft in the RAF is DHC Chipmunk WK518, which was delivered in Jan 52 (prototype flew 1946), and it appears to be in continuous use ever since, OR Spitfire XIX PM631, which never became a gate guardian (but was leased to Shorts). All of the other BBMF types have been out of RAF service at some point, Dakota was serving with the RCAF 'til 1971.
If you talk about type than it would probably be the Hurricane, as I'm sure LF363 and PZ865's service overlaps.
It's a complicated one isn't it...
Cheers
Charlie