I wouldn't want to fly via LHR instead of CPH. If you are worried about the connection time, which is plenty unless you are delayed, then simply take a flight one hour earlier as suggested by KSU.

At LHR you would need to go through security, but there is no passport control there unlike CPH. I have not transited at the new T2 at LHR, but knowing LHR they are experts at making things unpleasant. However, Star Alliance boasts that the MCT is only 60 minutes at LHR, so maybe it is not so bad to connect there?