Authorities mounted an emergency response and the coastguard agency said a helicopter, fixed-wing aircraft, lifeboats and nearby vessels with fire-fighting capability had all been called to the incident to help.
Thirty-two casualties have been brought ashore with ambulances waiting to take them to hospital in the port town of Grimsby, the chief executive of the Port of Grimsby East said via email.
It was not clear how severe their condition was.
The vessels involved are the US-flagged chemical tanker Stena Immaculate and the Portuguese-flagged container ship Solong, according to shipping industry sources.
The BBC cited the chief executive of Stena Bulk, Erik Hanell, as confirming that all the crew on the tanker had been accounted for.
Television images from the BBC showed at least one vessel ablaze with clouds of black smoke billowing into a grey sky.
The Royal National Lifeboat Institution (RNLI), a lifeboat service working on the emergency response, said: "There were reports that a number of people had abandoned the vessels following a collision and there were fires on both ships."
The collision took place in a busy stretch of waterway with traffic running from the ports along the United Kingdom's northeast coast to the Netherlands and Germany, shipping industry sources said.
Stena said its tanker was operated by US logistics group Crowley.
The tanker was one of just 10 enlisted in a US government program designed to supply the armed forces with fuel.
Maritime analytics website Marine Traffic said the 183-metre-long Stena Immaculate was anchored off Immingham, northeast England, when it was struck by the 140-metre-long Solong, which was en route to Rotterdam.
Two shipping sources said the Stena Immaculate was at anchor at the time of the incident.
Ship insurer Skuld of Norway would only confirm that the Stena Immaculate was covered with it for protection and indemnity, a segment of insurance that covers environmental damage and crew injuries or fatalities.
The United Nations shipping agency, the International Maritime Organisation, said it was aware of the situation.
with PA and AP