The first quake recorded was of 2.4 magnitude and measured around 1 mile deep at 5.37am on Sunday.
The second happened at 9.58am and was 4 miles deep and higher on the Richter Scale measuring 3.2 in magnitude.
Both were recorded 15 miles off the Lancashire coast near Fleetwood, which is 106 miles from Belfast and 114 miles from Dublin.
The Irish National Seismic Network (INSN) suggested it was down to a process known as glacial rebound.
People as far away as Dublin, Wexford, Wicklow and Kildare claimed they felt the tremors.
The INSN, which monitors seismic activity in the region, says the larger quake was the strongest quake recorded in Britain or Ireland since 29 May 2013 when a magnitude 3.8 earthquake struck off the coast of the Llyn Peninsula in North Wales.
INSN Director Tom Blake explained: "Although Britain and Ireland are far from any plate boundaries, much of the region is still experiencing quakes due to the removal of the weight of ice sheets that once covered the land.
"Occasionally this post-glacial isostatic rebound - the phenomenon of the land surface gradually returning to its pre-glacial contours - results in earthquakes of this magnitude, particularly in the northern half of the islands."
Further tremors are possible during the coming days but most are expected to be too small to feel.
An earthquake measuring 4.0 in magnitude struck 37 miles off the Co Mayo coast in Ireland in June 2012.