Yatsenyuk was at Downing Street for talks with British Prime Minister David Cameron.
Since taking office in 2010, Cameron's governments have reduced Britain's budget deficit, though the kingdom is still projected to be some years away from running a surplus.
"You know Mr Prime Minister, we have a lot in common with the United Kingdom," Yatsenyuk told Cameron.
"You passed austerity and you made your economy really vibrant and robust. We did the same.
"So we can share our experiences with Greece in order to make the world better, to keep the European Union united, to make the EU one of the key supporters of Ukrainian territorial integrity and of our independence."
After the meeting, Britain announced it would send around 50 troops to take part in a military exercise in Ukraine, in a show of support for Yatsenyuk's government.
Western powers accuse Moscow of arming a rebellion in eastern Ukraine and of deploying troops there. Russia denies the claims.
Some 50 British troops are to participate in the annual joint US-Ukraine led Rapid Trident exercise taking place in western Ukraine later this month.
"They will be focusing on vital infantry skills, tactics, mission command and headquarters," Cameron's spokeswoman said.
Cameron said: "Britain strongly supports Ukraine and Ukraine's right to exist in peace with its neighbours.
"We think the people of Ukraine should be able to choose their own future."
Yatsenyuk later spoke at Chatham House, the Royal Institute of International Affairs think-tank, in a speech entitled "Transforming Ukraine: Successes and Obstacles on the Way to Reform".
He said the Ukrainian economy needed austerity measures in order to become more robust.
The Ukrainian economy has taken a nosedive after three years of recession and more than a year of civil war.
Ukraine's national debt is expected to reach nearly 94 percent of GDP this year, according to the International Monetary Fund.
Yatsenyuk said his government was facing a battle against Russian-orchestrated propaganda.
He said Ukraine had not eliminated corruption, but had improved the transparency of its energy sector.
Yatsenyuk met US President Barack Obama on Monday, who urged him to follow through with tough economic reforms in order to meet its commitments to the IMF and other global lenders.