The 3 year law you quote may be so.
However,as you will need PP to keep/site the caravan on this piece of land (which the Council will NOT grant) there is no point in going further.
We have two instances of this in our country lane.
1.A very nice guy has two fields,and uses/used one to store his very small touring caravan.The Council told him to remove it,which (to save legal costs) he did.
2.Another guy is attempting to restore a "derelict" house,and had placed a mobile home on the land as a place to stay over whils rebuilding the property.
Again,the Council has served an enforcement order on him.He is appealing this order(I don't think he will win) and of course it is costing him a fair amount in legal fees.
The problem lays in the fact that if a caravan/temporary building is situated for the legal number of years without objection (in itself unlikely) then the land use changes to residentil.This means (in effect) that after that period the council must give PP for residnetial housing on the site,as it ceases to be grrenfield site.
The length of time you have owned the land doesn't affect this,it's how long the caravan/temporary building has been there that matters.
Councils ( all over the country) are very hot on this as they see it (quite rightly) as a backdoor way of flouting housing PP.