... I have been flying LHR-JFK/ORD a lot in the last few months, and 45 minutes is fine.

On my trip two weeks ago, I was 'admonished' by a young check-in agent (she looked younger than me - and I am 24!) that I should not leave it until so late, but I told her with the amount I travel, every minute I can spend OUTSIDE the ariport is time well spent. She made a face, but didn't say much else.

As GLD, you can check in at the Business Class line or Park Avenue, the latter of which is generally faster.