Public Health England (PHE) has warned the rise in Covid-19 deaths is "hugely concerning" as the UK sees the highest daily figure in four months.
The Government said a further 143 people had died within 28 days of testing positive for Covid-19 as of Tuesday.
This brings the total number of deaths in the UK to 43,018, according to Government figures.
It is the highest daily figure since 164 deaths were reported on June 10, but there is often a delay in the reporting of deaths over a weekend.
Separate figures published by the UK's statistics agencies show there have now been 58,500 deaths registered in the UK where Covid-19 was mentioned on the death certificate.
Dr Yvonne Doyle, PHE medical director, said: "The trend in Covid-related deaths is starting to rise quickly, which is hugely concerning.
"We have seen cases increasing especially in older age groups, which is leading to more hospital admissions.
"This is a stark reminder for us to follow the guidelines.
"Importantly, do not mix with others when unwell.
"We must all do our part to help control the virus by following the restrictions in our areas, maintaining social distance, wearing a face covering in enclosed spaces and washing our hands regularly."
The Government said that, as of 9am on Tuesday, there had been a further 17,234 lab-confirmed cases of coronavirus in the UK, bringing the total number of cases to 634,920.
Earlier on Tuesday, figures revealed a total of 321 deaths were registered in the week to October 2, according to the Office for National Statistics (ONS).
This is up from 215 deaths in the previous week, and is also the highest number since the week ending July 10, when 366 deaths were registered.
Some 106 of the 321 Covid-19 deaths in the week to October 2 were in north-west England – the highest number for the region since the week to June 26.
There were 40 deaths in north-east England, which was the highest for the region since the week to June 12.
Together these two regions accounted for 45% of all Covid-19 deaths registered in England and Wales in the week to October 2.
Just over 58,500 deaths involving Covid-19 have now been registered in the UK.
The latest ONS figures show that 53,335 deaths involving Covid-19 had occurred in England and Wales up to October 2, and had been registered by October 10.
Figures published last week by the National Records of Scotland showed that 4,276 deaths involving Covid-19 had been registered in Scotland up to October 4, while 906 deaths had occurred in Northern Ireland up to October 2 (and had been registered up to October 7), according to the Northern Ireland Statistics and Research Agency.