Do you think rear disc conversion would put the insurance up an awful lot?
Kind of depends on how the insurance looks at it.
Company 'A' might say that you have improved the braking performance of your car so are much
less likely to have an accident and your quote would be less
Company 'B' might say that because you have upgraded your brakes, you have increased the speeds at which you're likely to drive, are then
more likely to have an accident, so they will increase your premium
Oh, by the way, company 'A' doesn't exist
, or if it does I want their number!
On a serious note, some specialist insurers who deal mainly with modded cars won't necessarily put up your quote just for upgraded brakes, but the big companies probably will.
Not 100% sure on the DVLA, but I would say you didn't have to inform them, it's only for major things like changing the colour etc. (or anything else that is stated on the registration document).