Not sure I agree with you Dave, when cleared in, you will request and be given a prescribed route i.e. H4 - H3 and you are to follow the route (unless subsequently vectored by ATC to, for example, deconflict with other traffic), corner cutting isn't the norm regardless of your a/c type - the single engine rule applies to certain routes/areas because of the requirement to be able to land clear in the event of an engine failure...
"Whilst single engine helicopters must always follow the helicopter routes, it should be noted that multi-engine helicopters can be provided with an air traffic control clearance to transit elsewhere throughout the London CTR."
http://www.caa.co.uk/docs/7/EIS%2006.pdf