I would caution you to arrive earlier than 1 hour.

LH seem to be using a mish mash of gates at LHR at the moment, if you get the dreaded new gates (ie: gate 36 and up) then it is quite a schlep from security control and takes surprsingly long.

I don't check bags so cannot comment on bag drop -- there always seem to be an abundance of desks open in Zone K when I pass through on weekdays, the Business desks typically don't seem to have anyone waiting in line.