I have succeeded to check in with BA031 16/5 at 6:40pm uk time.
PCR or Lamp LAB Test Result
MUST give proof of Accreditation ISO 15189/UKAS
MUST Print out hard copies for everything
BA staff said you can do Lamp test in the airport on the same day. Result waiting time 1-2hrs (personal view, I think depends on how crowded it is on that day)
PCR is not accepted from the airport because they are not Accreditated with ISO15189/UKAS