I just followed up on a quote through Compare The Market, quote was £316.02 provided by LV. On their site I amend the start date by 4 days (moved to the 6th Jan instead of 10th) and it's raised to £355.77. That was the only change. So bear it in mind when going through these sites, get everything right. They refused to honour the first quote and lost my business.
That's what I've always understood to be the case, insurance gets more expensive the closer to the renewal date you get because they work on the principle that you have less time to shop around. I always get quotes 4 weeks in advance (about the earliest you can do most places).