"UK was discussing with Egypt at the moment exactly what action they are taking in Libya," she said.
The spokeswoman stressed that the UK's focus is on a political solution and there are no discussions beyond that at the moment within the government.
The UK needs to work with other countries to tackle the growing threat from Islamist extremists and their poisonous ideology, she added.
On Sunday evening, ISIL published a video showing the beheading of 21 Egyptian Coptic Christians who were kidnapped in Libya.
On Monday Egyptian air forces carried out airstrikes against IS targets in Libya.
ISIL is a militant group in control of large areas of Syria and Iraq. The group also has affiliates in North Africa. The group is well known for its atrocities, including posting numerous videos of the executions of captive foreigners on the Internet.