Have you checked, just for interest, the difference your insurance is going up by?
I just checked for me, with only 1 million and a 250 excess on insured risks website...
Without a claim in 3 years...
Insurer
Groupama Insurance Company Limited
Public liability
£ 65.00
With a claim in the last 3 years...
Insurer
AXA
Public liability
£ 108.00
That is a difference of 43 quid, for three years, 129 quid in total (note this is with 250 excess and only 1 million)
add on your 100 excess.
This means doing it through the insurance would cost you 229 quid. Doing it off the insurance would be 275 quid. It is so close a call I would check up on how much your policy cost will change before claiming.