As geeta said you don't need to fill out any forms. If you are within your customs allowance for flying to the UK (i.e. you're carrying no more than the allowed quota of alcohol, cigarettes, cash etc. and you have no fruit/veg/meat, and no other items to declare) then all you need to do after baggage claim is walk through the green 'nothing to declare' channel at customs.
I am thinking it will be conspicuous I'm a bit more than a tourist with so many bags.
But you're not a tourist, you are moving to the UK permanently on a settlement visa - they will be expecting you to have lots of bags.
It would only be suspicious if you were bringing 4 bags for, say, a 2-week vacation to the UK because it would look like you are trying to move to the UK illegally and so they would question why you need 4 bags of stuff for only a short trip.