A modest saving - but easy.

BeauBlock

My comprehensive motor insurance has been pretty cheap for a long time (old, no accidents etc and every year I do haggle or swap). This year I did the usual on receiving my quote for this year (£18 more than last year):  1. look on a couple of comparison sites recommended by MSE; find cheapest quote for identical cover 2. phone insurance company and give them the figures 3. DO NOT accept their first offer of a cut to their quotation 4. accept an offer they make near to or better than the best quotation from the comparison sites. This is pretty much what MSE recommends - it's just a bit shorter.
Result this year: £32 saving on their current quote or £14 saving on last year's premium. It's not much but it is very well worth having. Comprehensive insurance for two drivers with protected NCD, windscreen cover, courtesy car etc for £212 can't be bad.
PS Ironically, but not unexpectedly, one of the cheapest quotes from the comparison sites was from .... my existing insurers! I thought the government was going to stamp on that (new customers getting all the good quotes, existing customers being "fleeced").

MovingForwards

I secured a cheaper renewal just by phoning my insurance company, telling them I thought it would be cheaper and asking them to discount it.

Last month I replaced my car, 2 months after my renewal, and did a comparison search to see what the price would be; just under £189 fully comp, full protected NCB, windscreen cover, courtesy car, legal cover and commuting for the two of us, both have clean licences and no accidents etc. It was cheaper than my original car with my same insurer

I contacted my insurance company and they quoted me just under £155 on top of what I had already paid for my old car, eventually they dropped that down to just under £88 extra (both were including the admin fee). They also wrongly advised me if I cancelled and reinsured with them, they would refund the cancellation fee.

I cancelled my old policy, took the new one out and paid in full, got the pro rata refund and asked for the cancellation fee back. I still had change from the refunds after taking the new policy.