The Labour leader said the Government needs to “match the nation’s ambition” with a 24/7 rollout of jabs.
Sir Keir, who will visit a vaccination centre in Stevenage on Thursday, also urged the Government to increase capacity to four million vaccinations a week by the end of February.
Prime Minister Boris Johnson told MPs on Wednesday that the NHS will launch a round-the-clock vaccination service as soon as possible, despite Downing Street previously saying there was no clamour for a 24/7 model.
The Government has also said they are considering what further role community pharmacies can play, and Health Secretary Matt Hancock said on Monday that 200 would be coming on stream for vaccinations “very shortly”.
Sir Keir said: “The whole country wants this rollout to succeed. We were the first to get the vaccine and if we get this right and pull together, I know we can be the first country to roll it out successfully.
“To do that, the Government needs to match the nation’s ambition with a 24/7 rollout which harnesses all the expertise and dedication our country has to offer.
“Every high street has a pharmacy and I want to see every possible pharmacy deployed to help.
“Labour will play our part. Labour councils are already stepping up, supporting their communities and making generous offers of support to the Government.
“Across those communities, pharmacists stand ready to play their part too. Let’s use them, and let’s vaccinate Britain.”