I know of two people from different licensing areas who have applied in time for renewal of their FAC and have waited a long time for the renewal to be completed.
One person asked for a Temporary Permit and was told it would take as long to get the permit as for his FAC to be renewed. The other person's FAC runs out this coming Monday but may need a Permit.
The police seem reluctant to issue permits, my own area only issued one when I told them I shoot outside their area.
However, the instructions from the Firearms and Explosive Liaison Working Group say that Licensing Offices must notify FAC holders 12 weeks prior to an FAC expiry about renewal and that if the application is submitted eight weeks prior to run out and the Licensing office cannot renew in that eight weeks then a permit must be issued.
If you are having problems try quoting the link below, specifically para 3.5:
http://shootingshed.co.uk/wp/wp-content/uploads/2015/09/FELWG_Minutes-March-2015.pdf