How do I put forward a persuasive argument?

A key thing to remember when writing an English essay is that you need to back up every point you make. This doesn't have to be a hard-and-fast rule but try and think of the structure: Point-->Evidence-->Analysis (PEA). I like to spend five minutes with a spider diagram coming up with ideas in response to the question, and then put these ideas in an order that flows. Within those ideas you should then have multiples PEAs (think of it like peas in a pod!). The result looks a bit like this:

Question?

Pod/Idea 1: PEA x 3

Pod/Idea 2: PEA x 3

Pod/Idea 3: PEA x 3

The introductions and conclusions will hopefully naturally from this thought process. Also try to think of joining points between the separate Pods. 

This is obviously a rather mechanical way to go about things, but I find it a useful framewrok to start things off. English essays allow for a certain amount of fluidity so once you've come up with your central ideas, it's useful to think how you might nuance your argument. You may find that there are contradictions in the passage you're looking at that don't conform to a hard-line argument. Phrases like 'whilst in this instance xy, we can hardly claim z' help show an awareness that many texts are highly complex and tricky to force labels or judgements onto. 

For students aiming at higher grades I would recommend not only presenting an argument in response to the question, but also using the essay to query the assumptions made by the question. For instance, in this AQA question: 'Typically, texts about husbands and wives present marriage from a male point of view' Dicsuss in relation to 'The Taming of the Shrew'. Here there is a massive assumption in the idea of the 'male point of view' as 'typical' in Shakespearean texts. In fact, Shakespeare rarely presents a one-sided perspective of gender; the normalised male point of view has come from years of male-dominated Shakespeare scholarship, not the author himself.