GP understands NHS England is preparing an emergency response plan for the capital to cope with an outbreak if one does occur.
Londonwide LMCs said it would work with practices to make sure they were able to respond to the threat.
Londonwide LMCs medical director Dr Tony Grewal told GP it was 'only a matter of time' before the outbreak hits the capital, and that a large epidemic could kill hundreds of children. Many more could suffer life-changing complications.
He said: 'Constant travel between Wales and London means it is inevitable we will have measles in London. The only question is when, how severe will it be, and how we're going to deal with it.
'We should not be panicking the population, but people need to be aware that measles kills, measles maims, but there is highly effective and proven and safe protection available [the MMR vaccine].'
But he warned: 'Several hundred children may die if the worst predictions come to fruition.'
Dr Grewal said the outbreak could prove as severe as the swine flu pandemic, and called on the DH and NHS England to help prepare GP practices for the impact.
'I would like to see the NHS in London or the DH producing posters to go up in GP surgeries, making sure [GPs] have [vaccine] stocks to ensure that people who have changed their minds can have the vaccine. We must repeat that the science shows MMR is as safe as any medical intervention can be.'
Health officials have blamed widespread lack of protection against measles on the now discredited claims linking MMR with autism.
In some London boroughs, as many as 30% of young schoolchildren are thought to be unprotected.
Dr Grewal said the ongoing reorganisation of the NHS could in theory cause real problems if the large measles outbreak spread outside of Wales.
He said: 'The established channels of communication have gone. We've been working very hard over the last few weeks to establish new ones. All new re-organisations lead to confusion, but this has done so in spades.
'We are speaking to primary care leads in area teams, so there is communication there. If you look at how we responded to [swine] flu, people got down to doing what was important.'
He said practices should await further details on a contingency plan from NHS England's local area team and Londonwide LMCs due next week.
However, Public Health England (PHE) attempted to play down fears over a possible outbreak in London, saying there had been fewer cases there in recent years than other parts of England.
A PHE spokesman said: 'It is difficult to predict whether London could have a significant outbreak of measles like that seen in Swansea. Based on recent measles trends, it is more likely that London would have clusters of measles cases rather than a wide-spread outbreak as seen in Swansea.'
He said MMR uptake had improved in recent years due to a major catch-up campaign in 2005.
The spokesman added: 'Public Health England is working with NHS England, directors of public health and other health professionals in London to encourage uptake of the MMR vaccine where there are gaps.
'Parents of unvaccinated children, as well as older teenagers and young adults who may have missed MMR vaccination, should contact their GP surgery to have the vaccine as soon as possible.'
It comes as health authorities in Wales confirmed a 25-year-old man from Swansea who died on Thursday had measles at the time of his death.
Dr Marion Lyons, director of health protection for Public Health Wales, said: 'The tests confirm only that the deceased had measles at the time of his death. Further investigations are being undertaken by the Swansea Coroner to establish the cause of death.
'My sympathies are with the family at such a tragic time. Whatever the cause of death in this case, we should not be surprised if, as the outbreak grows, we start to see deaths in Wales. Measles is a potentially fatal disease and around one in every 1,000 people who contracts measles in developed countries will die.'
There have been more than 800 measles cases in Swansea alone.
NHS England had not yet responded to GP at the time of publication.