I don't think you can really make a case for that, look at the timeline.
Timelines are not the only evidential consideration. There is a lot of information that is only available by substantial investigative journalism.
As you said, UK was struggling and threw everything at a vaccine development. UK expects to pay £11.1 Billion on vaccines. The majority of that was a gamble with taxpayers money. Imagine if there had been little return. Only a small fraction of that was for purchase of vaccines.
Additionally, it would appear that AZ have given the UK deliveries higher priority because UK paid more per vaccine.
The Oxford-AstraZeneca vaccine is much cheaper, although neither the UK nor the US can match the EU’s $2.15 deal: they are expecting to pay about $3 and $4, respectively, per dose.
https://www.bmj.com/content/372/bmj.n281
Yet much has been made of AZ selling its vaccine at cost, but South Africa paid double price for the AZ vaccine
South Africa’s government found itself on the defensive this week after a senior health official revealed that 1.5 million doses of the Oxford and AstraZeneca vaccine just purchased for use among health workers would cost $5.25 (£3.84; €4.32) a dose, more than twice what the European Union is paying at $2.15.
https://www.bmj.com/content/372/bmj.n281
The explanation given is due to the investment in R&D for the vaccine:
“The explanation we were given for why other high-income countries have a lower price is that they have invested in the [research and development], hence the discount,” he added.
That principle has also been applied to the biggest players. The EU financially supported the development of the BioNTech and Pfizer vaccine and has obtained a lower price per dose ($14.70 than the US ($19.50).
https://www.bmj.com/content/372/bmj.n281
By that logic EU must have invested twice as much as others, including UK, into the AZ R&D.
Additionally, AZ, although claim to be providing the vaccine at cost during the pandemic, reserve the right to decide when that pandemic is over, and they will then increase their prices.
AstraZeneca and Johnson & Johnson have committed to not making a profit from the pandemic, while Moderna and Pfizer did not. AstraZeneca reserved the right, however, to declare the pandemic phase over and take profits from later vaccine sales.
https://www.bmj.com/content/372/bmj.n281
As I said, there is a lot on information that is being repeated, but there is much that is not available in the public arena.