Residents reported that buildings were shaking when the tremor hit shortly after 7.30am on Wednesday.
It is the second earthquake to strike the UK in less than two weeks.
Tremors of 4.4 magnitude hit Wales and were felt hundreds of miles away on February 17 – the country’s biggest quake for 10 years.
The epicentre of the latest quake was in Mosser, Cumbria, and it was also felt in Grasmere, Kendal, Cockermouth and Keswick, BGS said.
“One person reported hearing a thud and their whole building swayed from side to side,” a BGS spokeswoman said.
Another resident tweeted: “Just felt an earthquake tremor in Cumbria! The house shook for about 20 seconds.”
One person reported that the tremors felt “like something had hit the house”, while another said their bed had moved “as if someone was jumping around”.
It was the strongest quake to hit the region since 2010, when tremors of 3.5 magnitude were recorded in Coniston.
Seismologist Brian Battie told Sky News: “This part of Cumbria has experienced a number of earthquakes in the last 100 years.
“People would have felt buildings shaking and windows and doors rattling but I wouldn’t expect any damage.”
Earthquakes of around 3 magnitutude occur once or twice a year in the UK, BGS said.
The latest one was about 130 times smaller than the quake near Swansea last month, it added.
Mr Battie said the two events were not linked.
“Earthquakes occur fairly randomly,” he added.
The largest known earthquake to hit the UK occurred in 1931 near Dogger Bank in the North Sea, which had magnitude of 6.1.
The most damaging UK earthquake happened in Colchester in 1884 when 1,200 buildings needed repairs.