The capital was allocated £26m from NHS England’s GP Forward View fund over the next two years to boost coverage.
NHS England said future funding arrangements have yet to be agreed.
The GP Forward View plan, published in 2016, provides an extra £2.4bn a year to support general practice services until 2020-21.
Jane Cummings, NHS England regional director for London, said: “Appointments at evenings and weekends will not only improve access to GP services but will also help manage pressures on urgent and emergency care services especially over the busy winter period.”
But Helen Stokes-Lampard, chair of the Royal College of GPs, warned it was “simply impossible” for every GP practice to be open every night and every weekend.
She said: “Patients need to be aware that the scheme announced today will offer them a GP consultation, but not necessarily with their usual GP or at their own GP practice.
"It's encouraging to see investment promised in NHS England's GP Forward View making its way to frontline general practice, where our GPs and our patients need it – but we still have a long way to go until we have sufficient resources and numbers of GPs to deliver the care all our patients need and deserve.
"NHS England’s GP Forward View, which also promises an extra £2.4bn a year for general practice and 5,000 more GPs by 2020, could be a lifeline for our profession – but only if it is delivered in full and as a matter of urgency, in London and right across the country.”
