The UK gov site now states that you have to have a day 2 lateral flow test bought even if you’re only in Transit, you can’t use a NHS one. As faced with a similar issue, we bought an Excalibur one (which is approved by the UK gov and can be bought cheaper through the BA link) which means you have to just download their app, take the test and scan the result through the app, you get the result and a certificate which you can provide when asked.
