They couldn't, though.
27 member states (all bar the UK) signed up to EU collective bargaining for vaccine supply and a common approval process. The sign off for each vaccine has to be done by each of the 27 and then by the overarching European Medicines Agency. If any of the 27 want to use a non-EU preferred vaccine such as Russia's Sputnik, they can go it alone, which is what Hungary are doing.
Inevitably, the EU process has been bureaucratic and slow, with a focus on price rather than speed.
The situation has been neatly summed up by Bild, a German cornerstone newspaper. Here's what it is saying today, courtesy of the Guido Fawkes Order Order website.
“What did these three do better?” screams Bild’s headline under Netanyahu, Boris and Trump. The text makes it clear:
“Since the beginning of the corona pandemic, this trio has been silently mocked and ridiculed by the German government and the EU Commission. When it came to getting vaccinated, they put Berlin and Brussels in the shade [they] have the most successful vaccination campaigns in the western world on their feet. The fact is: as of January 26, Israel had 32% of its citizens vaccinated against the corona virus at least once. In Great Britain it was at least 10.6%, in the USA 6%. For comparison: Germany has 2%, the entire EU has 1.9%. …
The loss of German confidence was not helped when the first German vaccinated was vaccinated in England. This humiliation is reconfirmed in the breathless copy of Peter Wilke, Bild’s UK reporter, exclaiming that whilst he had not received a vaccination appointment in his home town of Mühlheim, he was shocked to get an SMS text from the NHS, “Suddenly I got a vaccination appointment in England!”
Undoubtedly, the Government has made some poor decisions regarding the pandemic but I don't see how anyone can reasonably criticise their handling of the vaccination programme. We're also one of the biggest donors to worldwide efforts to stop the pandemic in developing nations.