The short answer is: ask for their complaints procedure and do what it says.
As for what the procedure must contain:
As such they are required to comply with the independent school standards.
Those standards require: that a complaints procedure is drawn up and effectively implemented which deals with the handling of: complaints from parents of pupils and which—
(a) is in writing;
(b) is made available to parents of pupils;
(c) sets out clear time scales for the management of a complaint;
(d) allows for a complaint to be made and considered initially on an informal basis;
(e) where the parent is not satisfied with the response to the complaint made in accordance with sub-paragraph
(d), establishes a formal procedure for the complaint to be made in writing;
(f) where the parent is not satisfied with the response to the complaint made in accordance with sub-paragraph (e), makes provision for a hearing before a panel appointed by or on behalf of the proprietor and consisting of at least three people who were not directly involved in the matters detailed in the complaint;
(g) ensures that, where there is a panel hearing of a complaint, one panel member is independent of the management and running of the school;
(h) allows for a parent to attend and be accompanied at a panel hearing if they wish;
(i) provides for the panel to make findings and recommendations and stipulates that a copy of those findings and recommendations is— (i) sent by electronic mail or otherwise given to the complainant and, where relevant, the person complained about; and (ii) available for inspection on the school premises by the proprietor and the head teacher;
(j) provides for a written record to be kept of all complaints, and of whether they are resolved at the preliminary stage or proceed to a panel hearing;
(k) provides that correspondence, statements and records relating to individual complaints are to be kept confidential except where the Secretary of State or a body conducting an inspection under section 162A of the 2002 Act [i.e. Ofsted] requests access to them
Interestingly, the Government web site www.directgov.uk says this when talking about school complaints procedures:
Some procedures may allow for an additional stage if the local authority (LA), Diocesan Body (for Church of England or Roman Catholic schools) or another external agency provides an independent appeal or review. LAs are also required to set up a procedure for dealing with certain types of complaints, for example complaints about the curriculum or collective worship in a school.
That does not, of course, apply to academies/free schools. Unlike in relation to a maintained school, there is no right of complaint to the local authority about an academy/free school.