Central London Community Healthcare NHS Trust was caring for six 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 28 was up from five on the same day the previous week.
There were no beds occupied by Covid-19 patients four weeks ago in Central London Community Healthcare NHS Trust.
Across England there were 8,120 people in hospital with Covid as of June 28, with 205 of them in mechanical ventilation beds.
The number of Covid-19 patients hospitalised nationally has increased by 101% in the last four weeks, while the number on mechanical ventilators has increased by 72%.
The figures also show that no new Covid patients were admitted to hospital in Central London Community Healthcare NHS Trust in the week to June 26.