Southern Health Trust was caring for 35 patients with coronavirus in hospital as of Wednesday, figures show.
NHS England data shows the number of people being treated in hospital with Covid-19 by 8am on March 22 was up from 26 on the same day the previous week.
The number of beds at Southern Health NHS Foundation Trust occupied by people who tested positive for Covid-19 more than tripled in the last four weeks – 28 days ago, there were 11.
Across England there were 8,387 people in hospital with Covid as of March 22, with 172 of them in mechanical ventilation beds.
Nationally, the number of hospital patients with Covid-19 has increased by 5% in the last four weeks, while the number on mechanical ventilators has increased by 5%.
The figures also show that 40 new patients with Covid were admitted to hospital in Southern Health NHS Foundation Trust in the week to March 20. This was up from 35 in the previous seven days.