Labour Party member and NHS activist James Doran, who is on the walk, said he thought Scottish independence could help stop privatisation in England too.
He said: "A Yes vote would open the way for the NHS to be written into the Scottish constitution, preventing a government coming in and privatising it before voters have a chance to kick them out at the ballot box. This could be inspiration to the rest of the UK, giving a good example to those campaigning for a People's NHS."
Green Party campaigns officer Adrian Crudan, who is also marching, said: "The NHS [south of the Border] is fast becoming a brand name for a profit-seeking franchise rather than an integrated public service. Wake up and get out of the nightmare while you can - by voting Yes."
The People's March for the NHS mirrors the 1936 walk from Jarrow to London which was organised to protect against unemployment and poverty.
It is expected to arrive in London in six days after completing 280 miles. Its aim is to highlight concerns about the "rapid dismantling, privatisation and destruction" of the NHS in England.
It is one of a number of campaign groups which have sprung up.
Professor Sue Richards, co-chair of Keep Our NHS Public, which aims to prevent the NHS being transferred to private healthcare companies, said: "What's really happening in health is a drive towards the reduction of the role of the state in paying for and delivering health. We desperately want Scotland to stay together to help us escape from this. But if I were a Scot and lived in Scotland, personally I think I would be voting for independence."