I don't think they will rush. As a brit, I think this was all just hastily rushed through and approved by the government and the British medicines regulator (and only them as far as I'm aware, not the EMA or FDA, funnily enough) as part of a political stunt to trump the EU amid ongoing tensions over a Brexit deal, as well as to boost the government's dreadful approval ratings thanks to their poor handling of the virus. In a typical arrogant fashion, they claim that they will be known for "leading humanity's charge against the virus" in the future and one minister even said that "we're just better than European countries". It doesn't give me any confidence at all. Many European countries are rightfully holding out until there's more clarification from other drug and medical associations first. I don't think anybody from my side of the pond has much confidence in this given how quickly this has been produced. They're even demanding the PM and health secretary take it live on tv lol.
You don't play a political stunt with the lives of potentially a large percentage of the population. That's the kind of thing you go to prison for the rest of your life. They did make a clear and obvious break with the EMA and their slower processes, which can be seen as political middle-fingering, but the MHRA isn't a joke organisation that will be knowingly putting lives at risk.
That said, I'm a naturally cynical person in a lower-risk group, so I won't be rushing to have it. But I would say that with any initial vaccine. I'm more concerned how diverse the testing groups have been so far. Do they include pregnant women, people with cancers, various underlying conditions, children, auto-immune deficiencies, etc? Ultimately we won't know any longer-term consequences until the future. But governments will take a smaller amount of deaths and side effects in contrast to tens of thousands of deaths and a stagnating economy and way of life. That's one of those sad facts.
Yes there has been a degree of patriotism over passing regulations fast, something which I find ridiculous, but it's part of the sell.
I expect Boris to take it on live tv. That would be a big political play.