Exit T5 for a few hours before a connecting flight?

I am flying CPH-LHR arriving 08:30 and then onwards on a 14:35 departure LHR-JFK.

I need to pick up a book being held for me at the Sheraton Heathrow.

If I enter the UK through immigrations, take the bus to the hotel and pick up the book and then enter T5 with my boarding pass. Does that pose a problem?

My question centres on whether BA would do something terrible (like unloading me from the flight) if they do not scan my BP at the transit check point.

Does anybody know?

 

I've left T5 and re-entered before without an issue. I was inbound from the US on AA, landed in T3, transferred by bus to T5, cleared security, then ended up in arrivals and came back through. I also recently arrived T5 from elsewhere in Europe and had a departing flight to the US out of T5. Taking the train to the B concourse, I managed to make a mistake and end up back on the arrivals train and had to re-clear in B. Neither time did I have an issue, other than the annoyance of clearing security again.

 

Excellent. Thanks so much!