Boris Johnson said the new rules will be enforced by "tougher penalties".
The National Police Chiefs' Council (NPCC) says - in the 2 months to 17 August - there were 46 fines for breaching face covering rules (38 on public transport) in England and Wales.
13 fines were handed out for breaching social gathering rules outside local lockdown areas in August, and a further 36 were given out where there were enhanced restrictions.
And just 3 fines were handed out for people failing to quarantine after arriving back in England.
The Health and Safety Executive can also take action against businesses which fail to take appropriate measures to prevent the spread of coronavirus.
Up to 6 September, it carried out 14,900 spot checks resulting in action being taken in 2,500 cases.
Boris Johnson said: “The furlough scheme was far more generous than either Germany or France or virtually any country in Europe.”
Since September the government has been paying 70% of a furloughed worker’s salary, with the employer bringing it up to 80%. bbc.co.uk/news/explainer…
It will run until the end of October
It's difficult to compare generosity of schemes across Europe, because they vary between workers in some countries and because it's important to take into account normal support for workers as well as extra measures brought in for coronavirus.
Germany’s Kurzarbeit system usually pays 60% of normal salary (rising to 67% for parents) up to a limit of €6,700 (£6,000) per month
That's been increased until the end of the year, with those unable to work their normal hours for 7 months able to claim 80% of their salary.
The White House Press Secretary Kayleigh McEnany yesterday said: “Europe has 28% higher excess mortality rate” than the US. That's the number of extra deaths above what would normally be expected over a particular period.
Countries report these figures at different times and for different periods so comparing Europe as a whole is tricky.
The US saw a nearly 20% increase in excess deaths compared with previous years from the start of the outbreak in February up to 8 August.
Joe Biden has attacked President Trump’s record on job creation in Michigan - a key battleground state which was narrowly won by President Trump in 2016. We’ve been looking at US Bureau of Labor Statistics data.
Mr Biden, who was vice-president under President Obama, said: “We brought 80,000 jobs here to Michigan and the automobile industry.” Between January 2009 and January 2017, 79,100 automobile jobs were created.
Mr Biden went on to claim President Trump has “lost 50,000 of those jobs since he’s been president.” This is not true - just under 20,000 automobile jobs have been lost up to July 2020.
On testing, PM Boris Johnson said: "To date, we’ve carried out 15.4 million antigen tests. That’s more than any other country in Europe and more per head than other European countries like Germany and Spain."
The overall figure for tests to detect the presence of coronavirus in the body was 16.07 million, up to 2 September - according to government figures.
That's the number of tests, not the number of people tested, and the figure includes 1.4 million surveillance tests.
It is challenging to make direct comparisons (as countries may be counting testing in different ways).
But this total appears higher than the number of tests carried out in any other European country.
At #PMQs Prime Minister Boris Johnson and Labour leader Keir Starmer clashed over the government's coronavirus test and trace system.
Starmer said some people had been offered tests a long way away.
We've reported on recent examples of this: bbc.co.uk/news/health-53…
Boris Johnson said testing capacity had increased "from 2,000 a month in March to 320,000 a day".
As of 2 September, labs had capacity to process 369,000 tests a day, according to government figures
However, just under 250,000 of this capacity is reserved for Pillar 1 and Pillar 2 tests, or the testing used to diagnose whether someone currently has Covid-19.