Shakespeare had served his local community in Allesley for more than three decades and was an inpatient on the hospital's frailty ward at the time of his first jab, said it had been "wonderful".
Speaking on RTHK's Hong Kong Today programme, he urged people not to take a wait-and-see approach in case their favoured vaccines weren't available at a later stage.
Tsang said Hong Kong was sitting on a mountain of unused doses, while other parts of the world were "incorrect" to "compet for vaccines".
"They can not be used after the expiry date and the community vaccination centers for BioNTech will, according to present plans, cease operating after September".
"The whole world is scrambling for vaccines and its is not just right that we can buy a vaccine overnight and we just have it".
In a tweet paying tribute to him, the West Midlands Labour Party said: "We're sorry to hear of the death of Coventry Labour stalwart Bill Shakespeare". So far just 19 percent of the population has received one dose of either vaccine while 14 percent have received two doses. If people do not take the jab, Philippines will have to waste numerous doses.
Having received their second dose of the COVID-19 vaccine at least six months ago, participants will be randomized into groups to receive either a COVID-19 booster with 20vPnC; a placebo COVID-19 shot with 20vPnC; or a COVID-19 vaccine with placebo 20vPnC.
Stay-at-home order extended 2 weeks provincewide until June 2
But in order for restrictions to be lifted, the province will need to see a sharp decline in daily COVID-19 cases. As a result, the seven-day average of daily cases fell to 2,731 - its lowest point in about five weeks.
Hong Kong has purchased 7.5 million doses of the vaccine developed by the American pharmaceutical company Pfizer and the German company BioNTech, and an equal number of doses of the vaccine from the Chinese pharmaceutical company Sinovac, which has not yet been approved by the World Health Organization (WHO).
Hesitation is also common among health care workers in the city.
The territory now has around two million Pfizer shots that will be out of date in three months. A total of 3,263,000 doses of the Pfizer-BioNTech vaccines have been shipped to Hong Kong so far but only 1,231,600 have been administered.
Authorities also struggled to come up with incentives to encourage vaccination in cities where long quarantine measures and economically distressing social distance rules keep infections low.
Earlier this year, the government announced a HK $ 5,000 ($ 640) spending voucher for all residents as a way to boost the economy.
But on Tuesday, city leader Carrie Lam rejected the offer. The content is provided for informational purposes only.