Millions of pupils will return to the classroom on Monday for the first time since January, in the initial stage of the government’s ‘roadmap’ back to normality.
But experts have warned reopening schools will cause a rise in the reproductive number - or R value - of the virus, causing the number of infections to increase.
Dr Mike Tildesley, a member of the SPI-M group which advises the government, said the next few weeks would be “crucial" in the battle against the global pandemic.
"We do need to get this balancing act correct and we need to open up at the rate of vaccinations and keep the R number in check, as it were,” he told Times Radio.
"Definitely things are moving in the right direction but the next few weeks are going to be crucial for us to monitor what happens when schools open.
"Hopefully we can keep everything down and most importantly we can prevent seeing a rise in hospitalisations."
Parents should maintain social distancing and other rules while dropping their children off at school, he added.
"Just because you’re not in the home with your young children don’t use it as an excuse to go out and mix with other people that you otherwise wouldn’t have done,” he said.
"It’s possible with schools open we can keep the R number below one but if we are going to achieve that we all need to keep following all the other rules."
Falling Covid-19 rates are most likely due to the current lockdown measures, and the impact of millions of vaccinations "hopefully is yet to come", he added.
He said: "I think most of the reason the numbers are going in the right direction now is still due to lockdown.
"I think we haven’t quite seen the impact of vaccinations, probably start to come in round about now and having a little bit of an effect, but most of the effect thus far actually is probably the fact we have been under severe restrictions since the start of January."
Professor Sir Ian Diamond, head of the Office for National Statistics, warned that while lockdown had been a "success" the UK was "still not out of the woods".
"While we have seen major reductions, we are still relatively high,” he told BBC Radio 4’s Today programme.
"I’m in very much the view that we should do everything we can not to blow it nationally.
"We have done fantastically well in the last couple of months but we are not completely out of the woods yet."
He added that it was "very difficult" to separate the effect of the lockdown from the impact of the government’s mass vaccination programme, but it was clear both were playing a role.
Earlier Mr Hancock tweeted “thanks to the vaccine, we’re making progress”, as he urged everyone eligible to get a jab.