Do you have any unfinished business with them? Oustanding installments or a claim?
If not then you will have no issues, they are usually pretty quick at posting them out.
Did you get (and keep) a renewal letter? Apart from Swiftcover (who steal the years above 5 off you) that is sufficient proof of no claims for your new insurance company.
(Swiftcover will issue a proof of no claims with the correct entitlement but you have to call them specifically to get it. B*stards).