Cummings is a self-serving apparatchik with an eye to his future reputation so of course he’s trying to claim he was involved in the one successful program initiated by the government. I’m not sure why you give his claims any credence given his proven lies elsewhere.
I’m no fan of his and ad hominem arguments don’t help anyone. Considering the lack of transparency across the whole vaccine programme, I think the fact he made the point several times without being called out (in a committee hearing designed to call out any BS) is quite pertinent.
He lied to the public, repeatedly, in a very obvious way. He was also in that segment being fed softball questions by Aaron Bell, Conservative MP which were probably arranged in advance.
I therefore don't in any way trust his self-assessment of his own department's work and the 'vaccine task force' he set up, which incidentally hired some of his associates, who were paid very well, for example the PR firm:
A director of the public relations firm paid £670,000 to advise the head of the UK government's coronavirus vaccine task force is a longstanding business associate of Dominic Cummings.
Gosh, that article is incredibly revealing of some serious cronyism going on. It does also, however, confirm that the task force was operating outside of the DoH as per the original point.
If you trust what he says about who did what. If you don't, it could mean it operated outside the DoH but actually did very little in the procurement process.