Admiral's online system does now recognise imported DC5s correctly (at least when I checked a few weeks ago), however their entire service isn't that great - I've been insured with them in the past.
If you want to change anything in the policy, or rather anything to the car, you'll be stung for a silly amount of money for every change that you declare. Fail to declare, and your insurance is technically null and void, so you're driving without insurance bla bla etc etc you get the idea.
It may seem all well and good that the quote is cheap "on the face of it", but the specialist insurers have such a brilliant reputation for a reason - their customer care is fantastic, the staff are helpful and enthusiastic, their underwriters know exactly what they are doing and what they can afford to quote on and what they can't and their accommodation for adding mods is excellent.
If you do get a cheap quote with one of the big companies, then fantastic! If you're happy with the quote and the service levels they offer, good for you! No one is going to force you to go with a different company, it's your choice - all we can do is give advice and recommendations based on our own accounts with companies.
And as for the "wanting to know car history" question - every insurance company in this country should be asking this question - whether you can "handle" what is deemed as a powerful car and have a proven history of it will be a very big determining factor of the insurance quote.