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The Warwickshire local - who shares a name with the famous playwright - was given the jab at University Hospital Coventry in Warwickshire this morning.
As he watched Mr Shakespeare undergo the injection, health secretary Matt Hancock appeared briefly emotional, wiping a tear from his eye.
"It's been such a tough year for so many people," he said on Good Morning Britain. "And there's William Shakespeare putting it so simply for everybody, that we can get on with our lives.
"There's so much work gone into this. It makes you so proud to be British."
Bill, who is an inpatient at University Coventry Hospital's frailty ward, commented after his vaccine: "I need to say, the staff at this hospital are wonderful."
In pictures from the moment he was vaccinated, Bill could be seen wearing festive slippers and a dressing gown.
She received her injection at 06:31 GMT, making her the first person to receive one of the 800,000 Pfizer/BioNTech vaccines that will be administered in the coming weeks.
"I feel so privileged to be the first person vaccinated against Covid-19, it's the best early birthday present I could wish for because it means I can finally look forward to spending time with my family and friends in the new year after being on my own for most of the year," she said.
"I can't thank May and the NHS staff enough who have looked after me tremendously, and my advice to anyone offered the vaccine is to take it - if I can have it at 90 then you can have it too."
The vaccine, which is reported to have an efficacy rate of 95 per cent, was green-lit by health regulator MHRA for use.
It comes after Matt Hancock wrote on Twitter recently: "The MHRA has formally authorised the Pfizer/BioNTech vaccine for COVID-19. The NHS stands ready to start vaccinating early next week.
"The UK is the first country in the world to have a clinically approved vaccine for supply.
"Help is on the way."
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