The UKBA have issued advice to Libyans who do not fulfil the requirements of the immigration rules but wish to extend their stay in the UK
Libyans who wish to extend their leave under the Immigration Rules should apply in the normal way using the relevant application form. Where an individual is unable to meet some requirements of the Rules or provide some of the required evidence they should state why this is not possible, explaining any exceptional circumstances. Applications will be considered on a case-by-case basis and discretion can be used when reviewing cases.
Any Libyan national, with continuing lawful leave or previous lawful leave that has expired since 22 February 2011, who does not meet the requirements of the Immigration Rules but are unable to return to Libya may now be allowed to temporarily extend their stay in the UK.
Applications can be made on the FLR(O) form. Discretion may be applied in exceptional circumstances to grant a further period of leave for up to 6 months outside the Rules. Libyan nationals who are unable pay the necessary application fee should complete the ‘questionnaire for Libyan migrants of limited means’ . Please see http://www.ukba.homeoffice.gov.uk/sitecontent/newsarticles/2011/july/37libya-extend
This does not preclude Libyan nationals from claiming asylum if this is appropriate.