Can I visit London with the US visit visa I have (this is accepted in many countries I heard)?
You heard wrong. (Schengen transit visa is the only one where a US resident visa makes the Schengen transit unnecessary but I am unaware of any visitor visas which a US visitor visa can replace.)
Do British Airways provide any help in this kind of situation either to visit
No airline I ever heard of will help with visas.
or stay comfy at airport
Sure, there are lounges if you have no status and flying on economy then there are paid lounges provided by the airport, I believe you will be at Terminal 5, Aspire The Lounge is one I remember there might be more.