The Independent Works Union of Great Britain (IWGB) has called the walkout, which will start from 1pm on Tuesday.
The union expects hundreds of drivers to participate in the industrial action by not signing into the app.
Drivers will also be staging protests outside Uber's offices in each of these cities at the start of the strike.
IWGB said it was appealing for the public's support for drivers and asking customers “not to cross the digital picket line by using the app during the strike”.
Shadow chancellor John McDonnell retweeted an announcement of the strike posted by United Private Hire Drivers, a branch of IWGB, on Monday morning.
He wrote: “I support this strike for better employment rights and urge others to respect the app picket line.”
IWGB argues that Uber drivers should be classified as Limb (b) workers under UK law, rather than “independent contractors” as the company claims.
Drivers are demanding an increase of fares to £2 per mile from £1.25 per mil in London, and a 10 per cent reduction in commissions paid by drivers to Uber.
Workers are also calling for an end to “unfair app deactivations”, which they argue amount to de facto dismissals.
James Farrar, IWGB's united private hire drivers branch chair, said: “After years of watching take home pay plummet and with management bullying of workers on the rise, workers have been left with no choice but to take strike action.
“We ask the public to please support drivers by not crossing the digital picket line by not using the app during strike time.”
Mr Farrar was one of two employees who took Uber to court, in order to secure drivers’ rights to the national living wage, holiday, breaks and sick pay in 2016.
The case resulted in the High Court ordering Uber to class its drivers as employees, rather than self-employed, and afford them corresponding rights.
In 2017 Uber lost its first appeal against the ruling, although the US company has since launched a second appeal.
A spokeswoman for Uber said: “We are always looking to make improvements to ensure drivers have the best possible experience and can make the most of their time driving on the app.
“That's why over the last few months we’ve introduced dozens of new features, including sickness, injury, maternity and paternity protections.
"An academic study last month found that drivers in London make an average of £11 an hour, after accounting for all of their costs and Uber’s service fee.
“We continue to look at ways to help drivers increase their earnings and our door is always open if anyone wants to speak to us about any issues they’re having.”
A Court of Appeal hearing over workers’ rights at the company is due later this month.
Additional reporting by Reuters
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