Flew from Heathrow to Vienna on 1/10, and back on 10/10, with British Airways. Going out, uploaded my NHS Vaccine Passport which was exported from NHS App, onto the BA website prior to Check-in, but no other documents required. Upon arrival in Vienna, they checked the QR code on the NHS App on my phone and stamped my passport. Upon return, I had to complete the passenger locator form - and on that form had to provide the Day 2 test code and Vaccine Passport QR code, again from the NHS App. At check in, I simply confirmed these had been provided. At Heathrow, apart from a 15 minute queue for the e-passport gates, there were no checks and everything was very smooth. Generally, pretty hassle free. Vienna itself was a bit of a nightmare though - Vaccine Passports AND FFP2 masks for all indoor destinations. Talk about gold plating. They did accept the NHS Letter as proof of vaccination, or a paper printout of the NHS App. The App itself was kind of accepted, but they always tried to scan the QR code, which failed - however, a quick comment of "Brexit eh?" generally smoothed over any issues.