Following my conviction in August 2024 I had to sort out all my motor and home insurances. I thought I'd just note a few things here for others to read about more recent experiences, as many other posts here are rather dated.

Firstly, I found that ALL insurers WILL ask whether you have a conviction. Some may not actually ask the question directly, but it is listed under assumptions or in the policy booklets. Read all the small print!  I'm happy to be proved wrong, but this is what I found. Also, I wouldn't especially recommend using brokers, even those listed by Unlock. Those I did talk to didn't appear to have any specialised knowledge or access to useful insurers.
Price comparison web sites are good to start with - try them all! Then go to one, or more, of whatever comes up - but check carefully as often the information you put into the comparison site does not correctly get fed through.

What worked for me? This is not any sort of recommendation as too often peoples individual circumstances make all the difference. Also as I have no actual claims experience (good!) how they are in practise is unknown.

Car insurance: Admiral (multi car), don't ask for any details just whether you have a conviction. Strangely enough, they won't cover for house insurance with a conviction!
Motorbike: Honda Insurance (yes, I do have a Honda, but they may cover other makes), just ask if you have a conviction.
House: Homeprotect - they ask for details of conviction and sentence all on their web site quote page.
Caravan: Emporium - I spoke to them, they checked and came back with no premium increase from prior to conviction, so top marks to them!

In total my insurance costs have doubled. And of course I'll be reminded of this every year for quite a while yet.

Hope this helps others.