In reply to Tamati:
There is by the Castle and I've never had a problem parking but there are some double yellows and there are restrictions during the day. The wardens never seem to check but you never know whether this will change. The cafe car park (further down the road) is open until about 5ish and they let you park there but they do close the gate so make sure you get your car out in time.
Otherwise turn left into Lordship Park (from Green Lanes) and first left into Allerton Road where there are meters.
In the evening it's fine to park by the centre but gets busy ......