Even so it is a dodgy looking question. To ask, how can one can find out who they are insured with, is fair enough, but to post a reg when no one knows if it is the OP's doesn't make for easy feelings about it.
The DVLC should know ought they not ? Could try asking there.
Do you have a certificate of insurance? that'll tell you
when did you insure it?
How did you pay? if it's a bank direct debit, it'll show on your bank statement, if you paid by cheque, your bank still have the details if you no longer have the cheque stub - ditto if you paid by debit or credit card.
Phone your bank, give them your renewal date. They will tell you if you paid a significant amount of money out around that date. If they don't know who you paid it to, they can give you an originators code/ID. http://www.mib.org.uk/Motor+Insurance+Database/en/default.htm will help from there.