EU authorised Pfizer and BioNTech vaccines 21st December 2020:
https://www.ecdc.europa.eu/en/news-events/first-covid-19-vaccine-authorised-use-european-union
UK did so on 2nd December 2020:
https://www.bmj.com/content/378/bmj-2022-070344#:~:text=The%20UK%20became%20the%20first,adults%20on%2030%20December%202020.
So much of a cods up did the EU make over its authorisation and procurement processes (and so much of a panic did it get into because of its failures) that it threatened to close the Irish border (one of its “red lines” in the Brexit negotiations, if I recall) to vaccine shipments. This was because the UK had ordered its supplies from Ireland before the EU got its backside into gear and the EU was in danger of being sidelined:
https://www.theguardian.com/world/2021/jan/30/eus-vaccine-blunder-reopens-brexit-battle-over-irish-border
It was also noticeable that the EU instigated court action against AstraZeneca when it alleged that it had prioritised supplies of the vaccine over those to the EU. AZ argued that the UK contract was signed well before the EU one and that the EU contract stipulated that supplies were subject to its “best efforts” and not guaranteed. It took six months to settle the matter:
https://www.france24.com/en/europe/20210903-eu-astrazeneca-strike-deal-to-settle-vaccine-supply-dispute-out-of-court
Meanwhile the EU turned to Pfizer for its supplies. There is now an ongoing investigation by the EU’s Public Prosecutor’s office into the role played by European Commission’s President, Ursula von der Leyen, in the procurement of the vaccine supplies:
https://www.politico.eu/article/european-union-prosecutor-covid-vaccine-scandal-ursula-von-der-leyen/
There is little doubt that, had the UK still been an EU member, it would have been embroiled in all of this (and more besides). Whilst individual EU members were free to make their own vaccine arrangements, it was quite clear that any doing so would not have been looked on favourably:
// They chose not to because they are expected to show 'solidarity' - a requirement that we were free of.//
Exactly (and in fact, I believe none did).
The EU demonstrably failed in its efforts to secure vaccine supplies in a timely fashion. It's simply not geared up to doing things quickly. Any organisation that manages by committee is bound to find itself hamstrung in these circumstances and the EU in particular, trying to accommodate the needs and demands of 27 disparate nations is bound to suffer.
There are no lies in Mr Johnson's contentions.