Video report by ITV News Political Correspondent Carl Dinnen
The prime minister said he was "very keen" to get back to normal assessments in the coming school year.
Students have been marked based on predicted grades given by their teachers rather than the more traditional exams, which were cancelled due to coronavirus.
The system has come in for some criticism due to the lowering of grades for some individuals due to standardised weighting being applied, causing distress to some.
"I'm very, very keen that exams should go ahead as normal," the PM said during a visit to a school in east London.
"Exams are a vital part of our education and I thank all the teachers for all the preparations they are making."Clearly, because of what has happened this year, there is some anxiety about what grades pupils are going to get, and everybody understands the system that the teachers are setting the grades, then there's a standardisation system.
"We will do our best to ensure that the hard work of pupils is properly reflected."
Meanwhile, pupils who had their recent exam results downgraded by the Scottish Qualifications Authority will not all be expected to appeal, Nicola Sturgeon has announced.
Speaking at the Scottish government’s coronavirus briefing, the First Minister apologised for how exam results were dealt with.
She said: “I do acknowledge that we did not get this right and I am sorry for that.”
Speaking about problems with the SQA grading system, Ms Sturgeon said too much focus had been given to the system rather than individuals.
“We will be taking steps to ensure that every young person gets a grade that recognises the work they have done," Ms Sturgeon said.
“Our concern – which was to make sure that the grades young people got were as valid as those they would have got in any other year – perhaps led us to think too much about the overall system and not enough about the individual pupil.”
Nicola Sturgeon: 'We accept we didn't get this right'
Ms Sturgeon added: “That burden has not fallen equally across our society. Despite our best intentions, I acknowledge we did not get this right and I’m sorry.”
South of the border, Mr Johnson said he hoped schools would not be forced to close as a result of local action.
“I very much hope that doesn’t happen for any pupils but clearly what we are doing – the way we are trying to manage the Covid pandemic – is to have local measures in place and local test and trace to introduce restrictions where that’s necessary.
“But, as we have all said, the last thing we want to do is to close schools.
“We think that education is the priority for the country and that is simple social justice.”
The Prime Minister claimed on Sunday that there was a "moral duty" to get children back to school.
“It’s not right that kids should spend more time out of school, it’s much much better for their health and mental wellbeing, obviously their educational prospects, if everybody comes back to school full-time in September.
“It’s our moral duty as a country to make sure that happens.”
The Prime Minister struck a conciliatory tone to education unions, praising the work they had done to make classrooms safe.
ITV News spoke to the students impacted:
“It’s very important that everybody works together to ensure that our schools are safe and they are – they are Covid secure – I have been very impressed by the work that the teachers have done, working with the unions, to make sure that all schools are safe to go back to in September.
“A lot of work being done over making sure that there’s social distancing, bubbling, staggered start times, all that kind of thing.
“But, basically, the plan is there – get everybody back in September, that’s the right thing for everybody.”