Actually a deal is currently being negotiated to determine exactly how much they can tell us what to do, in return for avoiding the total destruction of our economy.

I'm not sure what Brexit has to do with this. The European Medicines Agency's criticism is entirely legitimate; they're criticising the emergency approval procedure to rush a vaccine into widespread application rather than not rush it.

Given Johnson and his government's inconsistent, perhaps even lackadaisical, response to the severity of the Covid-19 pandemic, it's not unusual that this emergency rushing be treated with skepticism — is it a good faith move to help immunise Britain or a way to save face for failing to properly implement lockdown quickly and early?

Any agency from around the world, not just in the EU, might hold the same skepticism and provide such criticism. It's only due to Brexit and modern Britain's tenuous relationship with the EU that such a knee-jerk rejection of such criticism might occur — but, given the actual topic of discussion should not be world politics but world health, it does seem inappropriately off-topic.