What does your partner think? It's very easy to blame yourself and think that removing yourself from loved ones and possible support is the answer. I am a partner and full time carer of someone with mental health problems.
No matter how hard it gets, I still want to be with my partner and know that without me, their health would decline. I would be sad, upset and heartbroken if my partner gave up on me without even talking about it after so many years of my supporting them.
If this is simply a case of you not loving your partner and wanting to end it anyway, that's fine, but you sound like you have not even considered how your partner feels.
Yes mental health can be draining on the ones who support you, but that doesn't mean they want to end it all with you.
If you speak with your partner and you both feel the end of the relationship has arrived then you have a few options.
1: Either get help from family and friends (either staying with them on a temp basis, or borrow the money to move out and then apply for HB)
OR
2:
You can move out before claiming HB as HB is paid in arrears. What you can do is apply for a crises loan to pay for the first month's rent and deposit and as soon as you move in, present the tenancy agreement to the council.
Obviously you will need to find a landlord willing to take you on but once you do that, you do not need to claim HB before you move out because the council realise you can only make a claim once you are in a place. The same goes for if you and your partner stayed together but moved out of the borough. Your old claim closes and you would have to make a new claim once in the new flat. You would then have 4 weeks for HB to be sorted and by the time the 2nd month of rent is due, HB will kick in.
Be aware though, that HB only pay a percentage of what most landlords charge (for example: My HB pays £168 a week for 1 bed flat if you are over 25, however NO flats are as low as that and we have to make the difference up)
I take it you are on ESA and Income Support? If you move out, you do realise you will have to shoulder all the bills yourself? Not easy when you are not well.
I have to take full responsibility for those as my partner just cannot cope with that. How will you? Who will support you to cope with that?
Also without DLA payments, your income is going to be rather low. Hiding away in a flat alone, won't help you. At least at the moment you have a partner and young kiddies around.
Sometimes being alone, is not the right thing to do.
Are you sure this is what you want? Or is this just feeling guilty? Is being away from your partner really going to help you get better? Or is staying with them and taking days out alone and doing activities alone going to be better?
If space is what you need, getting out of the house will do you good. Apply for the Health Wise scheme where you join the local gym or classes for about £12 a month and you work with a personal health advisor.
That did my partner wonders. Not easy I know! (I also suffer from Depression though not the same way)
Really think about this. Speak to your psych team/social worker or GP and also call SHELTER for housing advice.
Good Luck! :))