Pete, as you are already discovering there are two questions here.
Firstly, and to your credit you are trying to ascertain if the 6.5x55 with the loading(s) mentioned will result in a quick and humane kill on boar. The answer, as you will note from several respondents is a resounding yes - particularly from the european based forum contributors - although with driven boar the bigger the better as the saying goes.
The second can be answered with the following: Wild Boar have no specific primary legislation applicable, (as deer do with the Deer Acts), which dictate which calibres/muzzle velocity/energy/bullet weight must be used or when any closed seasons should be applied - the last being something which IMHO needs to be addressed sooner rather than later. Therefore, as Ogive has intimated, the legislation which offers them any protection is the all-encompassing WM(Protection)A 1996 and possibly the AWA2006, (although I'm not too sure how the later applies to shooting as it is more to do with animals rendered into captivity via cage traps etc.). Therefore, shooting and wounding them with an unsuitable (small) calibre might constitute an offence under the WMA 1996 if ever a prosecution was mounted, although I've got to say it would be highly unlikely to get anywhere even if someone had the evidence to get the ball rolling in the first place.
Given that there are no legal requirements regarding calibres etc. the arbitary .270 mentioned in the HO Guidance is parroted by whoever is next to write something regarding boar as you can see on the DI produced Best Practice. But just because it keeps getting repeated makes it neither law nor sensible, as you have noted by your investigation into the 6.5x55 versus .270 data. In answer to your question regarding anyone having less than .270 conditioned for boar, I have one simple condition covering all my rifles and ammo (including 12 bore slug) which allows them to be used on 'any other lawful quarry' which puts the onus on me to decide which calibre is suitable for which species. Now obviously I wouldn't use the .22RF on boar, but theoretically if I was sitting in a high seat with the .22/250 loaded with a suitable bullet weight/construction I could head shoot a pig - it would be my call. The .308 is obviously no problem with a suitable deer legal round and neither, for me, would the 6.5x57 I am looking to obtain this winter, and which has near identical ballistics as your swede.
If you are looking to approach your firearms department with a view to obtaining a specific condition for boar on your 6.5x55 then I would suggest that you prepare a supporting document that compares it to the .270 and maybe also include a bit of research about what the continentals are using. Either that or just go for the 'any other lawful quarry' and don't mention boar and see what you get.