I realise that you are looking for a club for singles, but I have been a member of the Motor Caravan Section of the Camping & Caravanning Club for a number of years and in that time we have welcomed many single ladies (and one or two single men) into our ranks. These ladies have remarked how welcome they have been made to feel and how helpful other members have been to them, both with advice and with more practical help. So, don't dismiss the more 'established' clubs when seeking camping venues. ;-)