The first is that from very early on the PM was flanked by medical professionals who appeared to be apolitical and were considered by all 'sides' on the vaccine debate to be honest (even if their opinions were sometimes contentious). That credibility meant they were listened to.
The second is that the NHS is almost a religion over here - this contributes to the medical profession being extremely well trusted.
In many places in the world the frontline medical staff are trusted but the system isn't. We're lucky here in that largely both aspects retain their respect. Note that I'm not commenting on other nations health systems or their population's opinion of it. We (the UK) are not unique in having reasonable healthcare; this is more about our high perception of the system providing it.
Finally, as a society we are very compliant, and also with the not-for-profit AZ vaccine there was a certain feeling of a national champion who was also helping to save the world.
Wakefield then ran away to US and Brits lived happily ever after ... till Brexit.
At least that's what's postulated here https://youtu.be/8BIcAZxFfrc