but an extra £120 and the only thing that changed as the street
They are allowed to charge you up to £75 as an admin fee, so probably part of it was an admin charge and it's wasn't entirely just a premium increase.
It could also be that the insurance price has generally increased and because you were in effect being requoted at current prices that you incurred the effect of higher prices all round rather than by moving street.

I don't believe they run their businesses from a random number generator !!

There will be reasons behind it even if we don't fully understand all the reasons.
One of those reasons will of course be profit as with any of us that are engaged in any kind of work or business.

So if you make an amendement you should expect an element of admin and profit to be usually included although companies do have different policies.