Where I am a Governor, we have an active Parents' Association and every parent is a member. It has a number of functions which include raising money, putting on events to help parents and children socialise and support the school by providing parent helpers when required. It is a very positive group but, as in many schools, does depend on people giving up a lot of time to organise events. Every time I go to an event, I do think the parents are very positive and cheerful about what they are doing. The children look forward to the events and I certainly think they would miss out if the Association was not in place. Some schools may well struggle to find enough parents who can do this. However, where my children attended school, the Association provided coffee and biscuits (for a fee) at Class Assemblies and at the Christmas/Summer Play, Sports Day etc which involved just a few parents and could be done at any school, if parents are willling. It would be a start.
None of the Associations I have been involved with have a teacher/parent relationship, other than sorting out logistics, room availability and suggestions for spending any money raised to complement spending priorities that the school has identified. The schools make it very clear, that individual parents are able to speak to teachers about any matter and this is the avenue to be used. The officers of the Association have no role in advocating for parents at all. This separates support for the school from complaints or discussions about individual children.
The school where I am a Governor has a similar approach but does have a Parent Forum. Parents are invited to attend and there is an Agenda which is produced by the Head and the parents have equal rights to place an item on the Agenda. For example, at a recent meeting, parents were concerned at how the Behaviour Policy was working and the allocation of House Points. It is a chance to speak to the Head in a semi-formal way on matters that are important to them. Sometimes parents who cannot attend, ask a parent to speak for them. The school also produces a weekly newsletter to keep parents informed.
As a Governing Body we also conduct Parent surveys and make sure we respond to any adverse scoring and comments. We do not want parents to think we do not actually read what they say. We do. We use Parent-Mail for communications where parents are expected to respond, eg booking into Parents' Evenings and curriculum meetings. Parent Governors are elected by Parents but do not represent them. Governors have a strategic role, not the day to day management of the school or taking up individual complaints with the Head.
I think if you find there are like minded parents who would like to start a Parents' Association (not a PTA as you probably will not get this) then you could approach the Head and suggest it. Start with small events (the Coffee and Biscuits as above) and see how you get on.
The Independent Prep School one of my children attended did have class representatives who met with the Senior Leadership Team once a term. However, these were never used to discuss individual children but would look at any item where it was felt an improvement could be made, e.g. morning snacks, dropping off arrangements, etc. so a bit like the Parent forum at the state primary school. Hope the above helps.