No CC @ weekends
Most places are free to park after 1800 (Becarful or Residents only Bays and weird times such as after 2000 or 0000. Always read the signage)
If you are going Central London on a weekend you will generally find a place to park if you arrive early (Shaftsbury Avenue, Soho, Victoria and surrounding areas). Can park along the riverbank easily.. or it was easy last time I was there for a boat party. If you arrive late expect all the theatre and clubbers to have taken up all the spaces. Weekday evenings is usually easy to find a spot.
Lots of London areas, but not all, provide free parking at weekends. Weekdays is for residents only and those who are visiting after 1800, 2000 or 2200.
If you do use Pay and Display Becarful of restrictions such as Maximum Stay times, its usually 2 hours max then you have to move.
EDIT: And if you are going to park as far away as Enfield you might as well leave the car at home as it will defeat the purpose. Its over 15 miles from Central and "Public Transporting It" will take around an hour.