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Probably. It assumes the trial will be successful both from an effectiveness perspective and side effects (roll something out to billions of people and a low rate of something undesirable happens a lot). I hope it is but I think we should plan that it isn't.
Even then I'm not sure how many doses will be available in September. First priority are health care workers and the over 50s. When they are vaccinated do we all go back to the office or not until your name gets to the top of the list?
No. I don't believe Alok Sharma either. Lots of people seem to be working on the assumption that something will change in that kind of timescale though and so things like school will be possible. I don't think it is very likely.