Current rates suggest that the vaccine rollout could be completed by 31 May. 3 weeks after that is 21 June. I don't see why that date isn't an reasonable expectation for a return to normality.
The key to normality is herd immunity, with the current efficacy of the vaccines, and using an unrestricted measures r number of 3, in order to to reach that threshold, over 90% of the population will need to have been vaccinated. Take up is less than that, because for a number of reasons a significant number are refusing to be vaccinated.
However, with all that said, and assuming we will fully open up international travel, then we're still not safe, until the rest of the world have also reached herd immunity.
I have seen various figures for the herd immunity threshold - I'm not sure if your one takes natural immunity into account?
I saw a report today of 90% take-up in the over 65s, which is still much higher than the models, which the current roadmap is based upon, have predicted. As more people are vaccinated, I suspect trust in the vaccines amongst the younger population will increase; this, combined with the desire to live normally, will have positive effects on take-up.
I'm not suggesting international travel will be fully reopened on 21 June. We'll likely have some sort of vaccine passport in place for that (I'm completely against a domestic passport, I should add, but that's a totally difference debate for a different place).
Bringing it back to TV - stage 4 of the roadmap (reopening nightclubs, theatres etc and ending all social restrictions) means that distancing will have to come to an end and this will inevitably be reflected in TV presentation.