You've probably had some PMs on this, country calls, but fradu is correct about the ownership of Saggy 699. She actually belongs to the RAF Museum Reserve Collection (RC). This has moved around a bit in recent years due to the depressingly continuous closures, such as Cardington, their former home. They are now at RAF Stafford but come under the jurisdiction of RAFM Cosford, as far as I know, and you should be able to contact them on 01902 376200.
699 is indeed the last "complete" Mk2 in existence and it is a shame if she does not have a dedicated group of volunteers taking care of her. As a dedicated preservationist in a slightly different field of transport, I can tell you that what you need is enthusiasts and donors in great numbers! When I was at LYE in April she was looking a little weathered but I put that down to the winter. Surely someone gives her a bit of TLC once a year for AOC's, or don't they do that any more? Anyway, I suggest you check with the owners for starters. I can't believe they intend her to go to scrap.
History-wise, 216 Sqn started accepting Comet 2s at LYE in July '56. The first 11 were earmarked for BOAC but none saw commercial service (re: Lukeafb1's post), and instead went to the RAF. After the ill-fated Comet 1s, BOAC waited for the Mk4s. XK699, the last of the "BOAC Mk2s", was built in '56 as G-AMXM, first flew on 02 Feb 57, and was delivered to (I think) 216 on 22 Feb - although I'm not sure whether the Testies had to try and bend any first, proir to Sqn delivery, as they did with our C130 Mk3 a couple of decades later!
The last C2 left LYE in '67. Perhaps Lukeafb1 can fill in here on any subsequent service with 51, which I believe went on into the '70s. For the record, the civil reggies for the Mk2s were, G-AMXA - M, and all became XKnnn, except 'D (XN453) and 'K (XV144) which were 2Es.
Anyway returning to topic, as you say, cc, you still have a bit of time in hand. Most restoration projects start after the event! There's no time like the present and I hope you gather a loyal following, bearing in mind that many will have more pressing worries to contend with. Let us know how you get on.