How you pay makes no difference whatsoever.
It’s all about the terms & conditions in the policy itself – the cheaper the insurance the worse they (usually) are. It’s all about internal costs – If you renew your policy & nothing happens for a year until you renew again then you’ve cost them nothing in administration etc If you dare to call them and ask them to do something then they charge accordingly.
In your example DezB, it is not unheard of for a renewal to be (say) £250, a mid-term change of vehicle costs another £200 yet when the following renewal comes through it’s at £275. The maths don’t stack up but, in their view, you are unlikely to renew at the nigh on double premium so they charge their ‘market rate’ knowing that they will charge you again if you make any changes. Sometimes this is driven by their use of generic call centres which they pay on a ‘per call’ basis – the more customers call, the bigger their bill.
There are all sorts of issues within wordings which are not apparent to the consumer – a favourite is insurers leaving out the normal Cancellation Clause. If there isn’t one then, legally, you’ve entered into an annual contract from which there is no get out and the entire annual premium is due to the insurer even if you sell the vehicle & no longer need the policy.
Better (sic) companies charge a bit more but their policies have this clause, do not carry administration or cancellation charges and make alterations on a pro rata basis.