Well using Compare the Market I got 128 quotes of which AXA were the cheapest at £363 but with a bigger excess and less benefits than LV's quote for £368, so no point in changing to AXA. I then tried Direct Line whose "Essentials" policy came in at £416 but when I added the benefits from LV Direct Line had risen to £555.
After this evening's searches for quotes all of which were more expensive than LV (£565 for our two cars) I don't think there's much out there that would give me any saving such that it is worth changing from LV.
Well at least the Triple Lock payment next April will help to mitigate our financial pain.