Covid boosters have been booked or delivered at nine in 10 care homes in England, according to NHS England.
Residents in more than half of care homes have received their booster jab already, it said in an update on the programme.
This comes after NHS England told GPs in September to prioritise offering Covid boosters to care home patients and staff by 1 November.
GPs have now visited around 6,000 care homes and are planning to visit a further 3,700.
It is expected that all residents who had their second jab at least six months ago will have been offered their booster jab by 1 November, NHs England said.
While some homes cannot be visited at this time due to norovirus or Covid outbreaks, visits are being scheduled for when it is safe, it added.
In total, more than four million eligible people have had their booster jab in the last four weeks, with GP surgeries filling in the gap after the closure of some mass vaccination centres.
Dr Nikki Kanani, GP and deputy lead for the NHS vaccination programme, said: ‘NHS staff are working flat out to vaccinate eligible groups ahead of winter – it is testament to them that just four weeks after we kicked off the booster rollout that we have already provided well over four million boosters to eligible people.
‘Not only that, but local general practice teams are going out to protect the most vulnerable – almost 90% of care homes have either already been visited or have a visit booked in for the coming days and weeks.’
Health secretary Sajid Javid said: ‘It’s fantastic that the vast majority of care home residents have had or have a visit booked to receive their booster jab.
‘I’m grateful to the NHS for rolling out these jabs so quickly, and for the continued dedication of the social care workforce. Their tireless efforts are helping us build a wall of defence across the country.’