Another way of addressing it would be from the point of view that you've already had your meeting, your request has already been agreed and you were awaiting written confirmation. I might be inclined to do that rather than say you haven't had your meeting yet, because that implies that it's reasonable for the process of consideration to start again. I'd probably prefer to emphasise that appropriate consideration and discussion has already taken place resulting in agreement.
I would write to appeal the decision on several grounds, firstly anything procedural they didn't follow, including reasons given for refusal, but also emphasising that the person best-placed to make a decision about whether your request can be accommodated and whether there are any genuine business grounds for refusing is obviously your line manager, who, after a meeting to discuss the request and how it might work, agreed it. HR are not in a position to make that decision.
Your manager advised you to put the request in writing to make sure you get the written confirmation of his agreement, but rather than the written confirmation you expected, you got a letter from HR refusing it, which shocked you.
You should also be prepared with counter-arguments as to why the reasons they give are not valid. Firstly there's obviously the fact that your manager clearly thinks there is no problem. Secondly, if, as you say, your job is basically redundant, then the argument that you have too much work to do that can't be given to anyone else can't be right. If they really don't need you at all, in your opinion, then you ought to be able to demonstrate quite easily how a slight reorganisation could accommodate a few hours less a week, which is all you are talking about. Obviously I don't think you should say you are basically redundant , but I'm just pointing out that if that is the case in your own opinion, it ought to be fairly easy to demonstrate how it could work, which is the whole point.
I think your manager is being rubbish, ought to take some responsibility for his decision making and stand up for you. It's ludicrous to think HR are the best people to make a decision, and yes they may have pointed out x, y and z issues that he may not have considered when agreeing your request, so in fact it might be the 'right' decision as far as they are concerned, but it's pathetic him taking no responsibility. Either he agrees with HR's opinion, in which case he should be apologising to you and acknowledging that, or he disagrees in which case he ought to be standing up to them. My opinion is they've probably pointed out some issues, and on reflection he agrees, but would prefer to completely blame them rather than have you cross with him.