National Health Service (NHS) national medical director Stephen Powis said the roll out of the vaccine across the UK would be a "marathon, not a sprint".
The government will issue doses of the vaccine to priority groups by age and health condition, meaning younger groups shouldn't expect to receive the shot until spring or summer in 2021.
Not only are infection rates and deaths still trending up in the UK, but now it seems people have grown weary of Covid safety restrictions.
Photos posted online in recent days show a rowdy crowd trying to force their way into the Harrods department store in London. The incident triggered fears of a terrorist attack.
One witness told the Sun newspaper he was setting up his coffee stand when "suddenly people started running".
"There were about 200 to 300 people, and I initially thought it was a terrorist attack," he said.
"When you're in London and everyone starts running a certain way, you think the worst. I know it sounds ridiculous, but you can't really know."
Other people described bottles being thrown and a security guard being punched.
Police were called to the store just after 1pm and four arrests were made for affray and Covid rule breaches, and the crowd later dispersed.
High-profile media commentator Piers Morgan led the outrage against the scenes, tweeting on Sunday morning: "Harrods yesterday afternoon. What a sick joke. Imagine how NHS workers feel seeing such selfish reckless behaviour?"
It wasn't just Harrods that was overrun with shoppers - more photos showed streets across London's shopping precincts packed with people on the first weekend after Covid restrictions were eased.
Plans to allow up to three households to meet in an extended "bubble" for a four-day period over Christmas have also been criticised as risky.
Foreign Office Minister James Cleverly said the photos of people ignoring social distancing were "frustrating".
"The vaccine, without a doubt, is a light at the end of the tunnel, but ultimately we still have to exercise personal responsibility," he told Sky News.
"We're not there yet, it will take some time to roll this vaccine out and it will take some time before we go back to normality."
Andrew Hayward, professor of infectious disease epidemiology at University College London and a member of the Scientific Advisory Group for Emergencies, echoed those concerns.
He warned the pandemic was "certainly not all over" and said it was likely the UK could still see a "severe peak" in coronavirus cases in 2021.
"We still have the winter to get through, which is likely to be the time that is most favourable for Covid transmission," Hayward told BBC Radio 4.
"We could still see very severe peak, particularly in January is when I predict that would be most likely, if we take our foot off the pedal on this.
"And that would be so sad, considering we're going to be in a stage where we can protect the most vulnerable during December, January, February and start to get back to normal in late spring, early summer."
Britain's latest Covid-19 figures show the virus is still running rampant across parts of the country.
The country recorded 17,272 new cases on Sunday, up by more than 5000 compared to the same time last week.
There were also 231 coronavirus deaths reported, which is an increase on the 215 fatalities recorded last Sunday.
Hayward said while the Covid vaccine would make a "massive difference", there were "still some unknowns and cause for caution".
He said one of the main concerns is not knowing how long the vaccine will provide immunity for.
"We know it will last at least three months. The strategy at the moment is to vaccinate those people at most risk of becoming critically ill and we know the vaccines will do that, so vaccinating those people will make a big difference to mortality," Hayward said.
"But if we want to start to impact on reducing the overall levels of the virus we need a vaccine that can help to also stop shedding of the virus and asymptomatic transmission.
"The proportion of the population that we would need to vaccinate to achieve herd immunity would vary a lot depending on whether or not it prevents asymptomatic shedding of the virus."
