It depends on the insurance company, and you may have to try more than one.
When you exchange your driving license, th U.K. one will have the date when you received your original license, so a brand new license might have a date of 1999 if that’s when you took your driving test.
You need to ask, but it would be unlikely that your insurance premiums go up ...
You don't need a UK driving licence to own, tax and insure a car in the UK.
I would highly recommend you to insure your car using your newly exchanged EU driving licence for the following reasons:
Your insurance company might request a copy of the driving licence you declared on the insurance policy when you make a claim;
DVLA might be notified of the ...