NHS England figures show 404 people had died in hospital at Royal Berkshire NHS Foundation Trust as of 5pm on Monday (January 25).
That was an increase of five compared to Sunday, when there were 399.
It means there have been 35 deaths in the past week, up from 33 the previous week.
The victims were among 8,870 deaths recorded across the South East.
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.