Insurance companies exist to make PROFITS.
They do this by taking in more cash than they pay out.
In your case, you have a CONTRACT with them, whereby in return for you paying them a premium, they agree to INDEMNIFY you in the event certain things happen, like the car is written off or stolen.
INDEMNIFY means they must place you in the same financial situation AFTER the loss as you were in just before the loss.
If the car was WORTH £5,500 they MUST offer to pay you that, like MUST. The have an enforcible CONTRACT with you that says so. The problem is agreeing the value at the time of the claim. You will probably be negotiating with a loss adjuster, and his first question will be to ask what you paid for the car. Tell him to mind his own business! DO NOT TELL HIM WHAT YOU PAID FOR THE CAR!!!
If you do, he will definitely offer less than that.
Taking it to an extreme (reductio ad absurdum) , if you had been GIVEN the car (so it cost you NOTHING) would that mean the insurance company could say you have suffered no loss and we ain't paying? NO WAY!!! You lost a Landy WORTH £5,500 and that is what they must pay, even if you made a good buy and paid only £2,000 for it.
NEVER EVER TELL AN INSURANCE ASSESSOR WHAT YOU PAID FOR A CAR.
Just start telling him what it was WORTH. If you can't agree with the assessor don't take any crap from him - complain DIRECT to your insurance company.
Trust me. You are paying a premium for INDEMNITY, not to be ripped-off.
CharlesY