From your question I can’t tell how much consultation you have already done on this. From the sound of it you are pretty sure that there is general support for your plans. However, there is a process to go through, and it takes time. As you are intending to change your finishing time you can only begin the changes at the start of the school year, so must back track from September to work out when you need to start the process.
I’ve written out the steps that you should take, based upon advice from GovernorNet
STEP ONE: consulting the local authority, headteacher and staff (including everyone employed as teachers or support staff at the school)
STEP TWO: preparing a statement the governing body must prepare a written statement proposing to make a change to session times, specifying what the proposed change is and when they would like it to start. The statement must draw attention to and include the Local Authority’s written comments as an annex.
STEP THREE: consultation with parents the governing body must circulate the statement to all parents of registered pupils at the school. Although you don’t have to, it is good practice for the governing body to circulate the statement to teachers and support staff as well. The statement must be accessible for anyone who wants to see it at the school. It should include information about arrangements for a meeting and be made available at least two weeks before this meeting takes place. Every attempt should be made to inform all parents.
STEP FOUR: arranging a meeting the governing body must provide an opportunity for all parents of registered pupils, the headteacher and any others they wish to invite to discuss the proposal at a meeting. The governing body must consider any comments made at the meeting, before deciding whether the proposed changes should go ahead or not and whether any amendments are necessary.
STEP FIVE: giving notice if the governing body then decide to go ahead with a change to session times they must inform the Local Authority and parents of all registered pupils of the change and when it is to take effect, giving a minimum of three months notice where the changes affect the start and finish of the school day and six weeks notice for all other changes (e.g. changing the times of the midday break)
STEP SIX: timing the new school session times must be implemented at the start of the school year where the changes affect the start and finish times of the school day and the start of the school term for all other changes