Well given your position outside of Coventry you may pick up some traffic going to ether Coventry or Birmingham airport but it's unlikely there is a popular route North South there as that would take traffic into Birmingham cta . As for the rules a helicopter must be at least 500 feet above any person,vessel or structure unless landing or taking off, if you are in Coventry itself then that goes up to 1000 feet . As for the noise limits new helicopters are designed and tested to be as quiet as possible older ones are not but I'm afraid you don't own the air above you house so they have every right to be there , unless of course you are getting this problem between 2200-0800 in which case different noise rules apply .
if you want to know what type of helicopters are flying over you maybe give Coventry a call as they should be taking to them