AFAIK, his thread is partially true. It isn't true AZ charges the same price to everyone (south Africa pays way more). Indeed, the Commission stepped in while the 'Vaccine Alliance' had already negotiated and agreed with AZ but it stepped in because several other Member States asked for it. They were concerned that their interests were not well represented by Germany, France and co, particularly on the price issue. So, they tasked the Commission to use part of the Emergency Support Instrument (limited to EUR 2.7 billion and it's not only for vaccines, it covers much more:
https://ec.europa.eu/.../coronavirus-vaccines-strategy_en) and negotiate on behalf of everyone. At that time, EU countries were afraid of competition among members and assumed the Commission could represent everyone's interest better.
It's worth noting this instrument is a down-payment on the vaccines that will actually be purchased by Member States, which is why the Commission had to negotiate within budget constraints. The price has always been a major concern for Member States, particularly for frugal countries, and countries whose economies aren't in good shape. This is why several EU countries have purchased fewer doses of Pfizer and Moderna vaccines - the most expensive ones - than they were eligible to buy. Poland, for example, ordered only 6.6 million Moderna vaccines despite being eligible for over 13 million doses. Bulgaria secured 500,000 doses, about two million fewer than it could have purchased. The Netherlands has almost entirely bet on AZ vaccine, which is why they started their vaccination campaign after the others. Of course it looks dumb now, but it also reflects years of under investments.
So, there are many factors explaining why EU countries are lagging behind in their vaccination campaigns, and I do hope there will be a real discussion about it. However, right now, I'm afraid most people are just looking for simplistic answers and scapegoats to score political goals, which is exactly Peston's case. I think it's reasonable to assume that any country, the UK included, would react in a similar way as the EU's if it faced a similar issue with AZ. I really hope we'll soon get rid of that mentality from too many people in Europe and in the UK consisting of reacting to anything with either "Ha, major failure for Boris Johnson“, or, alternatively, "typical ghastly EU lying out of jealousy of our success“. I'm afraid it will be very hard to reestablish trust after Brexit between the EU countries and the UK.