The Housing Secretary told BBC Breakfast the final goal of vaccinating all adults with one dose by the end of July was still on track.
Reduced numbers of vaccines are due to problems with worldwide supplies, a government minister has suggested - but he insisted the issues would not slow down the easing of lockdown.
"We legally signed a contract for delivery of the first 100 million doses here for people in the United Kingdom, as you would expect, both to ensure that people in the United Kingdom can get their jab and also because this is a UK-funded, UK-delivered vaccine".
Britain is using vaccines developed by USA drugmaker Pfizer and Anglo-Swedish rival AstraZeneca, with vaccine deliveries from Moderna expected to start soon.
Supply constraints are the biggest threat to Britain's vaccine rollout - now the swiftest among the world's major economies - and health officials warned that the programme would face a significant reduction in supplies from March 29.
The shortages come after Britain announced a new milestone Wednesday - more than 25 million people have now received a first shot of the vaccines developed by Pfizer Inc. and partner BioNTech SE or by Astra and the University of Oxford.
The vaccine shortage issue for AstraZeneca doses appears to be connected to a larger problem in the global supply chain, which is apparently impacting every batch of vaccines apart from Pfizer.
Prof Finn said the current aim was to complete priority groups 1-9 (aged 50 and above plus health conditions) but also "to deliver on those second doses because JCVI has been very clear from the outset that those second doses must be given in order to provide the long-term protection that people need".
It has been confirmed that there has been delays of 5m doses of the Oxford/AstraZeneca vaccine from India which is in part why there will be fewer doses over the coming weeks.
Britain's medicines regulator said there had been five cases of a rare type of blood clot in the brain among 11 million people given AstraZeneca's vaccine but said that it found the benefits of the shot far outweighed any possible risks.
While Britain tries to secure more vaccines, it is also facing growing anger from the European Union, which on Wednesday threatened to slap a ban on vaccine exports to Britain.
A letter to health leaders in England, published on Wednesday, warned of a "significant reduction in weekly supply" of the vaccine from March 29, "meaning volumes for first doses will be significantly constrained".
Hancock said that European Commission head Ursula von der Leyen had previously said that there should not be restrictions on companies who are fulfilling contractual responsibilities after Jenrick said he was "surprised and disappointed" with her comments.
Adar Poonawalla, the Serum Institute's chief executive, said countries were holding tightly to their supplies and restricting access to materials needed to make more.
Hancock told MP, "There will be no weeks in April with no first doses".
"We fully expect those contracts to be delivered on, because there are very significant consequences to breaking contract law".
Biden backs filibuster reform despite Republican threats
McConnell warned Democrats not to move any further, exposing the retaliatory steps he might take. "How about this", he threatened. Republicans would defund Planned Parenthood and sanctuary cities 'on day one, ' the Kentucky Republican continued.