South Warwickshire Trust was caring for 16 coronavirus patients in hospital as of Tuesday, figures show.
NHS England data shows the number of people being treated in hospital for Covid-19 by 8am on June 21 was up from 10 on the same day the previous week.
There were five beds occupied by Covid-19 patients four weeks ago in South Warwickshire NHS Foundation Trust.
Across England there were 6,002 people in hospital with Covid as of June 21, with 149 of them in mechanical ventilation beds – though none were at South Warwickshire Trust.
The number of Covid-19 patients hospitalised nationally has increased by 29% in the last four weeks, while the number on mechanical ventilators has increased by 5%.
The figures also show that 26 new Covid patients were admitted to hospital in South Warwickshire Trust in the week to June 19. This was up from 12 in the previous seven days.