The most recent deaths happened at care homes in Shropshire, according to the data from the Office for National Statistics.
There have now been 219 coronavirus related deaths at Shropshire care homes and a further 77 in care homes in Telford & Wrekin.
No new deaths have been reported at the county's health trusts, where 595 patients with coronavirus have died since the start of the pandemic.
It includes 554 deaths at Shrewsbury and Telford Hospital NHS Trust, 34 at Shropshire Community Health Trust and seven at The Robert Jones and Agnes Hunt Orthopaedic Hospital near Oswestry.
A further 253 deaths have happened in Powys, ONS data shows.
The cumulative number of hospital coronavirus deaths, by NHS trust, in the Black Country, Birmingham and Staffordshire as of March 29. By date of death, not the date the death was announced. Data: NHS England.
A spokesman for NHS England said: "A further 40 people, who tested positive for coronavirus (Covid-19) have died, bringing the total number of confirmed reported deaths in hospitals in England to 86,234.
"Patients were aged between 31 and 97 years old. All except one patient – aged 59 years old – had known underlying health conditions.
"Date of death ranges from December 19, 2020, to March 29, with the majority being on or after March 25.
"Their families have been informed."
Meanwhile, 29,033,640 vaccinations have been carried out across England to date – including first and second doses.
In the Midlands, 5,068,688 first doses of the coronavirus vaccine has been administered, while 499,636 second doses have been carried out.
The data includes vaccinations carried out between December 8 and March 29.