As I stated in my response of 16 June 2021 to the hon. Member's Questions 14221, 14222 and 14223, throughout 2011, the UK Government sought to respond to rapidly changing and volatile dynamics in order to protect Libyan civilians and wider UK interests. The UK's objective was clear: protect civilians and promote stability in Libya in accordance with the UN Security Council Resolution 1973, in support of NATO's Operation UNIFIED PROTECTOR.
As announced in Parliament by the then Foreign Secretary on 26 April 2011, the diplomatic mission in Benghazi was expanded to include an additional military liaison advisory team. This team was deployed to support the Libyan National Transitional Council (NTC) on how to better protect civilians. The team advised the NTC on how to improve their military organisational structures, communications and logistics. This deployment was fully within the terms of UNSCR 1973; both in respect of civilian protection and its provision, which expressly ruled out a foreign occupation force on Libyan soil. As stated by the then Foreign Secretary, "their sole purpose is to support the NTC's efforts better to protect civilians by advising on military organisational structures, communication and logistics. They are not involved in training or arming the opposition's fighting forces, nor are they executing or providing military advice".
Turning to your question concerning contact with the Libyan Islamic Fighting Group, there are no records of any UK contact with this group, in fact, the Libyan Islamic Fighting Group was a proscribed terrorist group in both the UK (in 2005) and US (in 2001).