You have been very lucky to get just an FPN. However, it may still cause you trouble. On the one hand the according regulations state: "Where the applicant is of good character in all other respects caseworkers should normally be prepared to
overlook a single minor unspent conviction resulting in (...) a relatively small fine or compensation order, [or] a
fixed penalty notice. (...) Receiving one [an FPN] does not form part of a person's criminal record as there is no admission of guilt." However, it also states "caseworkers should
not normally disregard any conviction that falls into the following categories irrespective of the severity of the sentence imposed: a. Offences involving dishonesty (for example,
theft, fraud)". See
this document. You definitely have to declare it if you apply within 5 years of the incident, and success of your application depends on caseworkers discretion (always a gamble). Since this was a small issue and dealt with in form of an FPN, it will not be an automatic knock-out criterion, but your chances have been diminished. If you want to play it safe, wait until the incident is 5 years in the past.