I'm in the Soho right now, but it was a bit of a struggle.
I'm BA Gold (OW Emerald) and the first agent told me that her computer was telling her "No". But she said it was her first day and she didn't know what the various statuses mean or what the lounge rules are so she passed me on to a colleague.
Her colleague's computer also said "No" butNthe colleague said it didn't "sound right" so consulted another colleague who assured her that, no matter what the computer says, I do get access. And I was in.
Now, the AA app is telling me that it's 65 minutes to gate 14, via the train. I'm sure that it's just downstairs.