Each application is dealt with on its own merits so it is not possible to give a specific time scale. In some instances it can take up to 4 months depending on any medical issues, convictions etc.
Firearm licenses are difficult to get, see the gov.uk website for details. You need to be registered with a GP and part of the checks involves your medical records. There will be an interview and possibly a home inspection - more likely in your case as you won't really appear UK systems for a while.
Permits for personal protection also allow the holder to carry their firearms concealed. Northern Ireland is the only part of the United Kingdom where personal protection is accepted as a legitimate reason to obtain and own a firearm.