The Independent report said Britain's electronic eavesdropping centre GCHQ (Government Communications Headquarters) appeared to be using high-tech equipment on the embassy roof to intercept German data.
The broadsheet cited aerial photographs and information about past spying activities in Germany, as well as documents provided by Edward Snowden, the former contractor with the NSA who has fled to Moscow.
The report comes hot on the heels of a furore over claims that the United States tapped Merkel's mobile phone as part of worldwide surveillance operations.
A US eavesdropping post on the roof of the US embassy in Berlin is believed to have been shut down last week as Washington scrambled to limit damage from the row, the Independent reported.
A spokeswoman for British Prime Minister David Cameron's office said: "We don't comment on intelligence matters."
Germany's Foreign Ministry meanwhile asked Britain to respond Tuesday to the reports.
The ministry said in a statement that Britain's ambassador was "invited in" at the behest of German Foreign Minister Guido Westerwelle.