The paramedics will ensure the patient is on a trolley, chair or wheelchair.
They will then inform nurses, after the 45 minute window has elapsed, that they are leaving to respond to more life-threatening call-outs or other emergencies.
The letter, obtained by ITV News journalist Paul Brand, came from Diana Lacey, director of Urgent and Emergency Care (London) at NHS England.
It states: “Due to the significant amount of time being lost to the London ambulance service when patients wait for a lengthy period before being handed over to ED (Emergency Department) staff, and the risk this poses to patients waiting for an ambulance response in the community we have been seeking further opportunities to release ambulance crews waiting to handover patients.
“From January 3 we are asking that...any patients waiting for 45 minutes for handover and are not in a cohort are handed over immediately to ED staff allowing the ambulance clinicians to leave and respond to the next patient waiting in the community.
“If the patient is clinically stable the ambulance clinicians will ensure that the patient is on a hospital trolley or wheelchair/chair and approach the nurse in charge of the emergency department to notify them that the patient is being left in the care of the hospital and handover the patient.”
Major hospitals already have a clinical responsibility for patients at the point of clinical handover or 15 minutes after they arrive at hospital by ambulance, whichever happens earlier.
Responding to the leaked letter, Liberal Democrat health spokesperson Daisy Cooper said: "This move shows the shocking reality of the NHS crisis and is yet further proof that a major incident must now be declared across London.
"The Health Secretary must act now to save the capital’s hospitals from being overwhelmed.
“The Government needs to recall Parliament immediately, declare a major incident and above all else, pass a plan to get the country out of this health crisis before more people die."
Ambulances are having to wait outside casualty departments at many hospitals in London and across the country as doctors and nurses inside the A&E units struggle to cope with the number of patients.
A spokesperson for the NHS in London said: “The NHS is experiencing record demand for urgent and emergency care. We are working across London to speed up ambulance handovers at hospitals - where it is clinically safe to do so - so ambulance crews can get to more people who are unwell in the community.
“This is one of many ways we are strengthening the NHS response this winter, along with more beds, extra 111 and 999 call handlers, more ambulance clinicians and expanding the use of 24/7 control centres across the capital for urgent and emergency care."
London acute hospitals are being asked to aim for a maximum of 45 minutes for handovers however this is not a “blanket policy” and decisions should still depend on clinical judgement.
Dr Adrian Boyle, president of the Royal College of Emergency Medicine, has suggested that between 300 and 500 people are dying as a consequence of delays and problems with urgent and emergency care each week.
He stressed: “We need to actually get a grip of this.”
Ministers and NHS chiefs have challenged these figures.
Nearly 38,000 patients waited more than 12 hours in A&E for a decision to be admitted to a hospital department in November, according to figures from NHS England.
The London Ambulance Service is understood to have lost almost 32,000 hours in handover delays between July and September last year.
Downing Street said that the Government is doing "everything possible" to increase the number of beds available amid concerns about pressure on the NHS which was facing an “unprecedented challenge”.
The Prime Minister's official spokesman said: "The NHS is already maximising its number of beds, so the equivalent of 7,000 additional beds, plus funding for discharges and increasing virtual wards. That's all to free up capacity.
"Again, that's all thanks to the extra funding, the billions of extra pounds we've put in.
"We are doing everything possible to increase the number of beds."
He insisted that the Government has been "up front" with the public about the pressure the NHS would face this winter and denied there was a funding shortage despite waiting lists of more than seven million, chaos in many A&E departments and people struggling to see GPs.
He said: "I think we are confident we are providing the NHS with the funding it needs - and as we did throughout the pandemic - to deal with these issues.
"I think we have been up front with the public long in advance of this winter that because of the pandemic and the pressures it's placed in the backlog of cases that this would be an extremely challenging winter, and that is what we are seeing."
He emphasised that the pandemic was among the biggest causes of the current pressures on the NHS, but also pointed to delayed discharges as a reason.
He said it was an issue the Government had "recognised and have been seeking to address this year with additional funding into the system".
Asked if the Prime Minister thought the NHS was in crisis, his spokesman said: "This is certainly an unprecedented challenge for the NHS brought about, as I say, by a number of factors."