I owned a Sunbeam Tiger twenty-five years ago and would never ever want another one. Its a pain to work on, handles terrible, often over heated and needed fairly constant attention. If you want a British V8 I'd recommend a Triumph TR8. I own one now and its night and day compared t the Tiger. The TR8 is almost like a modern car despite being 30 yrs old. The TR8 was designed with a V8 engine in mind while with the Tiger it was an after thought.
Back in those days it was quite customary to hot rod them or even take a Sunbeam Alpine and convert it to Tiger specs and nobody really cared. . Back then Tiger owners were a an electic fun group of hot roddin' beer drinkin' good old boys but nowadays some Tiger owners are quite anal retentive about originality. These types want to believe they've got some sort of a near AC Cobra, but that's just not the case.
Prices for Tigers have gone up quite a bit so be careful that you are really purchasing an original Tiger and not a converted Alpine if it is being advertised as a Tiger. You'd expect to pay more for a Tiger than a conversion. so you'll take a beating on resale if it turns out your "Tiger" is a converted Alpine. There is a website that lists original serial numbers and subtle differences to look for, so I'd check it out. For fun factor its not an issue, but a good Tiger is around 35+ K or so nowadays and you wouldn't want to unwillingly pay that for a conversion.
Once again my advice is go for a TR8, but if you're set on a Tiger then educate yourself about them before purchase.