St George's day never has been a public holiday. Nor has St Andrew's Day or St. David's Day.
Public holidays to celebrate this sort of event do not really work, except in peasant societies where the whole village will celebrate together. But in modern urban societies the significance of the day will be lost.
Far better to celebrate, but not have a holiday. That way, children will be in school, but will have special events that day to mark the event. Ditto in workplaces.
Because the British have not ever been liberated from an oppressor (e.g. Bastille Day in France), or have had a significant event in the past to do with the birth of the nation (e.g. 4 July in the U.S), we have never really "done" national days.