In the end stayed with More Than, but saved £100 by getting a quote from their website, then ringing back to the renewals team. Apparently, they can't budge on the renewal price that's generated, but if you seek a fresh quote on the internet they can use it. I guess you just get a new policy number rather than a renewal of the existing policy. Not sure what the difference is, except that it was £100 cheaper for exactly the same cover and excess.
Just thought this might be helpful info for others to know!