With that one, unfortunately not possible for a couple of reasons.
a) They don't leave much fabric in the seams to let out, meaning you'd get an absolute maximum of 1cm extra across the back, so if the top two buttons don't do up now I'm afraid it's just too small to have anything done with it.
b) You say the jacket is vintage - the seams will have been hot pressed and will have set - you won't be able to get the creases out
c) It'd be expensive and you'd need an extremely good seamstress, and it's likely to be more hassle than it's worth unless it's a Bernard Weatherill jacket which are over £1200 new.
If that's the style you want, take photos and keep looking for one a bit bigger. My Mum could copy that (she copies wedding and formal evening dresses with ease) so I'm sure there's another seamstress that could if you can't find one to fit.