The Labour leader has urged anyone who is eligible but wary of a third dose to “consider the impact of their decision, think again, and get vaccinated".
Speaking ahead of his own jab on Monday, Sir Keir said getting the booster was “vital” to support the NHS over winter.
He explained: “It is frustrating and worrying that medics are seeing too many hospital beds and NHS resources are taken by those that have chosen not to get the vaccine.
“I am calling on those who are eligible but unwilling to get vaccinated to consider the impact of their decision and think again.
“We are stronger when we all come together and act to protect ourselves, our loved ones and our communities from the virus.”
“But with the number of vaccinations down a quarter from the peak earlier this year, we simply cannot afford for the Government to take its eye off the ball in speeding up the rollout of the booster programme.
"The Prime Minister needs to break the habit of his tenure by stepping up and getting a grip.”
His intervention comes as Labour analysis revealed that the total number of booster vaccinations currently being administered remains significantly below the number of jabs delivered at the same point in the first vaccine rollout earlier this year.
During the initial vaccine rollout, the number of vaccinations peaked at 602,265 a day on average.
In contrast, the current total number of vaccines now being delivered per day on average is 435,542, over a quarter less than in March.
It comes as Scotland recorded one coronavirus-linked deaths and 2,067 new cases in the past 24 hours, according to the latest data.
The Scottish Government said Public Health Scotland is aware of an “ongoing processing issue with UK Government lab tests which may impact on cases and tests” in the daily figures and investigations are under way to resolve the problem.
The death toll under the daily measure, of people who first tested positive for the virus within the previous 28 days, is 9,649, but the Scottish Government said registry office are generally closed at the weekend which can impact figures.