Look for companies that do NCB 'mirroring'
Really its just a case of doing the comparison site legwork (whilst being careful with the phone numbers and email addresses you give them as no matter how many boxes you tick you'll get spammed to buggery)
Some sites ask more/different questions that others and in this case the ones that make the difference are ones that actually ask if you're a named driver on anyone else's policy.
As you're example above though saying they're giving you a discount and actually being cheaper aren't the same thing.
A thing to be aware of though is the mirrored no claims is useful this year - next year it'll probably be trumped by your own accrued NCB... which will of course only be one year. So you might not be able to get as good a deal next year as you can this.