Put down that crackpipe son, seriously...
You can apply for a shotgun licence legally, yet you need a very good reason for one to begin with and I don't think "personal defence against zombies" would stack up really. Best bet is to get in touch with your local PCSO and get proper advisement on your suitability for such a licence. My sister is a PCSO and can assess people for shotgun licences.
Once you have the licence, getting the gun is the easy bit.
As a SGC holder i can tell you, you dont need a very good reason to hold a SGC, I use mine for rough shooting and for clays, but you would have to be mentally ill or have a criminal record not to get a SGC. You HAVE to have a very good reason for wanting an FAC though, including being a member of an approved gun club.