Lots of prices and policies are changing on 31st Dec and 1st Jan. Generally they will all be increasing in price. I saved about 70 by renewing a basic plan 2 days early.
My parents this year changed from Aviva hospital level 2 to Aviva 16.1. The plans are very similar. The saving was about 800 each, 1200 rather than about 2000. This plan was found by a broker.
If renewing early some insurers can only start a plan on certain days, ie I could renew my plan with Aviva on the 30th Dec (Tuesday), I couldn't on the 31st Dec (Wednesday).