1 hour transit time to the airport? You need to get a new helicopter pilot.
Seriously though, you're forgetting timezones. Hop on the jet at 11am NYC time and be in London at 7:30pm London time. Leave London at midnight and be back in NYC at 10:30pm NYC time. You're not going to be exhausted from travel because it's first class all the way and you don't even need to pack bags.
Many bigger cities seem to actually be surprisingly lacking on viable (and legal) landing sites for helicopters... Trust me, I've tried.
You may not be exhausted but sitting stationary for 7 hours just to get dinner doesn't seem like such a fun thought, even in first class. (The novelty wears off very quickly)
Seriously though, you're forgetting timezones. Hop on the jet at 11am NYC time and be in London at 7:30pm London time. Leave London at midnight and be back in NYC at 10:30pm NYC time. You're not going to be exhausted from travel because it's first class all the way and you don't even need to pack bags.