You don't need a drivers details to make an insurance claim, just a reg number. With that being said, you've made a mistake by letting your insurance company know about the incident. You're now classed as "high risk" and regardless of fault or claim, your insurance premiums will increase at renewal for the next five years. Expect a 20-30% hike as a minimum. Technically. you're supposed to let your insurer know about any "incident", but for minor bumps and scrapes (similar figure to your excess) you'll end up financially worse off if you do, considerably so.
For cosmetic damage, I would never let my insurance company know, if its just a bit of scratched chrome, take it to a body shop and let them fix it.
Anyway, your choice now is, make a claim against the other driver, this will be settled as 50/50 by the insurance companies, as without any independent witnesses it will be impossible to prove who was at fault (you could have rolled back into him). Otherwise, do nothing, pay for your own repairs and suck up the renewal increase. DO NOT make a claim within two months of your policy renewing, an "open" claim on your policy will put you into the highest risk category and your renewal will be a minimum 5X your current quote.
I used to work for one of the "Big Six" insurance companies.