The likely targets would be internet service providers, governments, the private sector and critical infrastructure, according to a joint statement from the British National Cybersecurity Center (NCSC), the FBI and the US Department of Homeland Security.
The imminent attack was not, however, linked to allied nations' missile strikes on Saturday in Syria, Britain's Press Association (PA) news agency reported, citing White House cybersecurity coordinator Rob Joyce.
Britain and the US have previously flagged responses including fresh sanctions, indictments and online retaliation.
"We are going to push back," PA quoted Joyce as saying.
Russia was threatening the US and Britain's safety and security, the two countries said in their joint statement.
"Russian state-sponsored actors are using compromised routers to conduct spoofing ‘man-in-the-middle’ attacks to support espionage, extract intellectual property, maintain persistent access to victim networks and potentially lay a foundation for future offensive operations," the statement said.
"The UK Government will continue to work with the US, other international allies and industry partners to expose Russia's unacceptable cyber behaviour, so they are held accountable for their actions," PA quoted NCSC chief executive Ciaran Martin as saying.
Earlier this month, NATO warned it would use its collective defence mechanism for only the second time if it were hit by a devastating cyberattack.