Spa in fact SHOULD be Open until 2pm
I just got connected through the Exec Club here in the USA to a charming BA agent at Heathrow - he called the arrivals lounge at T1 and was told that the spa is indeed open until 2pm. He was concerned about the error on the website and asked for the url so they can get the time corrected.
He also assured me that hot breakfast is available until 2pm (although I wonder if that is a SHOULD rather than a reality).
I look forward to seeing reviews from fellow flyers experiencing the Elemis treatments (especially if after noon!), including length thereof (am I truly reading that it's possible to get a longer treatment if one pays extra?)