Thanks guys. The issue isn't the hosting, just what I'm paying for. Like all companies my hosting company don't tell you that you're on an old plan and that there are cheaper alternatives available - i.e. more or less the same benefits but less price. Only came across this when I popped on to their online chat facility and asked. Will work out around £40 - £50 less per year.
So have to purchase the new hosting first, move the site over, then cancel the old hosting.
Will mean I'll have to put the site in to maintenance mode so no new posts can be made - backup and migration should only take a few hours. The big downtime is the time it takes for the new DNS to kick in, this can take up to 24 hours.
I'm probably looking at somewhere between Boxing Day and the 31st - old hosting is due for renewal of the 2nd January so have to get it cancelled before then.
I'll hopefully be able to give plenty of notice.