Rofa,
Not your fault, it's a common misunderstanding about an aerodrome licence which I'd like to correct.
LCY have a licence 24/7 365 from CAA Aerodrome Standards. They publish their operating hours in the the UK AIP. The weekend Families Day takes place outside of the published hours and is only available to a/c not requiring the use of a licensed aerodrome.
LCY have local rules about who what and when can operate there; some of which are linked to the Planning Permission.
Any airport owner can set rules and waive them - it is after all their land.
To operate un-licensed one would have to either send the document back to the Belgrano with a stamped envelope asking for it back each Monday or issue a NOTAM - neither of which are in fact practical.
I've always been unhappy that, during the week, LCY seem to take the attitude that an SEP is not safe to operate in and out, yet have a charitable change of mind for the day. A bit like flying Spitfires etc over Buck Palace too.
Wonder what the risk assessment looks like?
Sir George Cayley