Hi Jimbob,
A caravan mover is likely to demand 40A of current just to get the caravan moving for a fraction of a second, once it is moving the current demand falls rapidly to typically about 15 to 20 A. If you are trying to go up a steep hill the current will stay higher.
Typically most caravanner's will only need to use the mover for a total of about a minuet once on site, but even if it were longer say 5 mins, the amount of power used will only be about 20A for 5/60, of an hour or 1.6Ah. Allowing for multiple start currents when making fine adjustments it is very unlikely to exceed 2Ah in total. This is like running a 12W bulb for two hours.
Even 85Ah leisure batteries should be able to cope with this level of discharge. The question is how much power will all your other appliances use, and ultimately they are likely to use much more than the mover.
If you use caravan sites with electric hook ups, then I think an 85Ah battery will be more than man enough to run you mover. If do not have a site with hook up then you may need a bigger battery especially for longer stays.