The hospital said it was “grateful” for the shift, while a leading People’s Vote campaigner said he believed it would increase the focus on the demonstration’s importance.
“We’ve got a new date for one of the biggest and perhaps most important demonstrations our country has ever seen,” Labour MP David Lammy said.
“We’re changing the date because we’re determined to change the course of history. This is a march for our future, our country and our democracy.”
Mr Lammy said the Brexit crisis now boiled down to “a simple question”, adding: “Can we allow Boris Johnson to force no-deal – or another scorched earth form of Brexit – on our country, without all of us having our voice heard?”
Mr Johnson has promised a “do or die” Brexit on Halloween, even if, as now seems near-certain, he cannot strike a fresh deal with the EU.
Staging the march on 19 October also means it will be held just 24 hours after the end of a crucial European Council meeting, which is likely to be the last chance of a last-gasp deal.
Otherwise, Mr Johnson is insisting on a crash-out 12 days later, unless a cross-party alliance of MPs can find a route to thwart him, in a showdown No 10 expects to take place on 9 September.
'Let Us Be Heard' follows the 'Put It To The People' demonstration on 23 March, when up to 1 million took the Final Say message onto the streets of the capital.
More than 100,000 demonstrators joined the first People’s Vote march in June 2018, some 700,000 took part in the 'March for the Future' in October 2018.
The next rally is intended to be the culmination of a nationwide campaign in cities and towns around the UK being staged throughout this summer.
Organisations behind it include youth groups For Our Future’s Sake (FFS) and Our Future, Our Choice as well as the European Movement, Open Britain, Wales for Europe, Scotland for a People’s Vote, People’s Vote North, Wales for Europe, Ethnic Minorities for a People’s Vote, LGBT+ for a People’s Vote and more than 100 grassroots groups from Aberdeen to Cornwall.