NHS England figures show 941 people had died in hospital at Sheffield Teaching Hospitals NHS Foundation Trust as of 5pm on Tuesday (June 1).
That was an increase of one compared to Monday, when there were 940.
It means there have been two deaths in the past week. The previous week there were no new deaths recorded.
The victims were among 13,357 deaths recorded across the North East and Yorkshire.
Daily death counts are revised each day, with each case backdated to the actual date of death.
This means some of the deaths that were first recorded in the latest period may actually have taken place days earlier.
NHS England guidance states: "Confirmation of Covid-19 diagnosis, death notification and reporting in central figures can take up to several days and the hospitals providing the data are under significant operational pressure."
Only deaths that occur in hospitals where the patient has tested positive for Covid-19 are recorded, with deaths in the community excluded, such as those in care homes.
Boris Johnson has insisted there is “nothing in the data at the moment” to prevent ending Covid-19 restrictions later this month, as the proportion of deaths involving the virus fell to the lowest level in eight months.
But the Prime Minister warned there is a need for caution, saying there is “no question” of an increase in infection rates.
Latest figures from the Office for National Statistics (ONS) show 9,860 deaths from all causes registered in the week ending May 21, and of these, 1.1% (107 deaths) had “novel coronavirus” mentioned on the death certificate.
The last time the proportion was so low was in the week ending September 11, when the virus accounted for 1.0% of deaths, according to PA news agency analysis.
At the peak of the second wave, in the week ending January 29, Covid-19 accounted for 45.7% of registered deaths.
The figures come on the same day it was confirmed 75% of UK adults across the UK had now had their first coronavirus jab, and 50% of adults in England had received both doses.
A total of 39,585,665 first doses have now been delivered since the vaccination rollout began almost six months ago.
This is the equivalent of 75.2% of all people aged 18 and over.
Debate is continuing over whether the final stages of unlocking restrictions in England can go ahead on June 21, due to concerns over the spread of the coronavirus variant first identified in India.
Mr Johnson said on Wednesday that there was “nothing in the data at the moment that means we can’t go ahead” with the next stage.
But he warned: “We’ve got to be so cautious because there’s no question, the ONS data of infection rates is showing an increase.
The Prime Minister said: “We always knew that was going to happen, don’t forget, we always said that the unlocking steps that we’ve taken would lead to increases in infection.
“What we need to work out is to what extent the vaccination programme has protected enough of us, particularly the elderly and vulnerable, against a new surge.
“And there, I’m afraid, the data is just still ambiguous.”