Of the 500 Londoners who were vaccinated on Tuesday, the first day of the vaccine programme, 194 got the jab from the Guy's and St Thomas' NHS Foundation Trust, chief executive Dr Ian Abbs told a board meeting on Wednesday.
Dr Abbs said the start of vaccinations was "a great moment for our country and a great moment for Guy's and St Thomas'".
Half of those vaccinated in the atrium at Guy's on Tuesday were aged over 80.
Prime minister Boris Johnson visited Guy's Hospital on Tuesday to see the vaccination hub in action, as did NHS England chief executive Sir Simon Stevens.
Chief operating officer Jon Findlay explained that Guy's Hospital at London Bridge will have three 'pods' each capable of administering 600 jabs a day, giving a total daily capacity of up to 1,800 people, with availability of the vaccine likely to be the main constraint.
As of Wednesday, Guy's and St Thomas' had received an initial consignment of 975 doses of the Pfizer vaccine.
The NHS South East London Clinical Commissioning Group – which covers Southwark and Lambeth – has warned locals not to contact their GP surgery to enquire about the vaccine, but wait to be invited by the health service.
A total of 253 patients who tested positive for COVID-19 have died in the care of Guy's and St Thomas' since the start of the pandemic.