Best share dealing platform?

My husband recently got his ILR (yay!) so now I would like to find a home for some of the savings which have been sitting earning pretty much nothing for the last 5 years.

I came across this list of share dealing accounts during a quick search but would really appreciate hearing of any personal experiences.  Who do you use and are you happy with them?  https://uk.stockbrokers.com/guides/share-dealing-accounts

Does anyone have any suggestions or recommendations they wouldn't mind sharing?  Thank you!

We have shares which are managed through Equiniti Shareview.  Our shares are handled through them because they were distributed as part of a privatisation scheme (we received free ones and bought some on option), and the process was handled through Equiniti.  I have not shopped around, but we should do that now that my husband is changing jobs.