They will be joined by drivers in the US cities of New York , San Francisco, Chicago, Los Angeles, San Diego, Philadelphia and Washington DC in striking over pay and work conditions.
The protests come days before the company lists its shares on the New York Stock Exchange.
Uber said drivers were “at the heart of our service”.
The United Private Hire Drivers Branch of the Independent Workers Union of Great Britain (IWGB) said the nine-hour boycott of the app would take place between 07:00 and 16:00.
In the US, members of the New York Taxi Workers Alliance will strike from 07:00 to 09:00 local time. There, Uber drivers will be joined by members working for Lyft and other taxi-booking apps.
Union branch co-ordinator Lydia Hughes joined Uber drivers in their strike today.
“They’re going public and their founders are going to make billions off the hard work of Uber drivers who make the app run,” she told World Service radio. Drivers “are demanding rights, a minimum wage, holiday pay and there’s no reason they don’t deserve that.”
The unions would like to cut the commission the taxi-hailing apps take. The IWGB in the UK said it would like Uber’s commissions to be reduced from 25% to 15% and for fares to be increased to £2 a mile from about £1.25.
The NYTWA in New York said it wanted commissions of 15% to 20% and better job security.
“I’m striking for my kid’s future. I have a five-year-old son, and I drive for Uber to support him,” said Sonam Lama, a NYTWA member and Uber driver since 2015.
An Uber spokeswoman said: “Drivers are at the heart of our service – we can’t succeed without them – and thousands of people come into work at Uber every day focused on how to make their experience better, on and off the road.
“Whether it’s being able to track your earnings or stronger insurance protections, we’ll continue working to improve the experience for and with drivers.”
The company has argued previously that it is transparent when it comes to pay and that drivers have earned more than $78bn (£59.7bn) since 2015, as well as $1.2bn in tips since tipping was introduced on its software in July 2017.
Uber last month warned it “may not achieve profitability” when it released details of its share plan listing.
Uber said that its most recent annual sales rose to $11.2bn and losses narrowed to $3bn.
But it also said it expected operating expenses to “increase significantly”.
The company did not disclose how it will price its shares on 9 May, but it is reportedly targeting a range of $48 to $55.
That would potentially give the 10-year old firm a value of up to $100bn, making it the biggest initial public offering this year.
Uber is also expected to raise about $10bn through the flotation.
Last year, Uber lost an appeal against a ruling that its drivers should be treated as workers rather than self-employed.
In 2016 a tribunal ruled drivers Mr Farrar and Yaseen Aslam were Uber staff and entitled to holiday pay, paid rest breaks and the minimum wage and the ruling was upheld by the Court of Appeal.
But Uber pointed out that one of the three judges backed its case and said it would appeal to the Supreme Court.
Please include a contact number if you are willing to speak to a BBC journalist. You can also contact us in the following ways: