How to get mental health support for a man who doesn't want it?

[NotHerRealNames]

I want my partner to see a GP over his mental health, but he won't go. He also won't sigh up for counseling or support groups.

Do I have any other options here?

He isn't a danger to himself or others.

Honestly OP, no.
If he isn't a danger to himself or others then you have very few options.
Does he have any friends or family who could try and encourage him to get help?

Unfortunately, no. It's really hard to watch someone struggle and not be able to help. I hope he is able to realise he needs help soon.

It's very difficult.

In order to do psychotherapy you have to be in a place where you know you have a problem and want to look at it and think with the therapist about your part in it.

Doesn't sound like your partner is in that sort of place yet.

Is it affecting him so he can't pull his weight at home?
Is he working/not working due to it?
It can be really frustrating especially if they are happy to vent to you but not do anything constructive about it.

Just ro add - assuming it is affecting you, and you have told him this clearly, if he takes no action, then you should (and are entitled to) take steps to protect your own MH and wellbeing. Eg you are allowed to,and should, do things like socialising even if he doesn't want to. If he is not taking action to help himself, that doesn't oblige you to bend your life out of shape to accommodate his inaction.

It's more affecting his work. He has a decent salaried job. He broke down the other night snd confessed that he hasn't done anything at work for two months due to his low mood. His work hasn't realized yet, but it will surely catch up with him soon.

His dad is unwell and likely to pass away soon, which I believe is the cause of all this.

Hmmm, you have my sympathies OP.
I have a DH just like this.
Different causes, but the effect is the same.
It takes its toll on you, for sure.
Sorry, but I have no answers other than to take care of yourself, whatever that entails.