If the claim is settled, most insurers put the amount of the claim on the no claims bonus statement, along with date, type of claim and status.
How much was your claim for and is it fully settled? If there was personal injuries claimed for it's likely not settled yet. If it's not settled yet you really are handcuffed for a while.
If your bonus went from 5 to 3 years what you had on it was 'step back' protection. That is a level below 'full' bonus protection and generally a less expensive addition. Some insurers have step back protection for free e.g. Eaglestar.
Axa are quoting at present where there is a claim under a certain amount, I think it's 10k, not sure.
Provided they would quote you anyway and there is no other reason they would decline it on (vehicle type, drivers age etc). Ask your broker again. Though if claim is not fully settled, not a lot they can do.