NHS England figures show 364 people had died in hospital at Frimley Health NHS Foundation Trust as of 5pm on Tuesday (July 14).
That was an increase of one compared to Monday, when there were 363.
It means there have been two deaths in the past week. The previous week, there were no new deaths recorded.
The victims were among 3,468 deaths recorded across the South East.
Of 25 trusts within the region, Frimley Health trust has the second-highest death toll.
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 last 24 hours 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.
Across England, the death toll hit 29,127 on Tuesday, up from 29,105 on Monday.
Separate figures from the Department of Health and Social Care show 291,373 people had tested positive for Covid-19 across the UK as of 9am on Tuesday, up from 290,133.