AIBU to feel stuck being 'homeless'?

@theeyeofdoe the council may provide emergency accommodation temporarily to avoid a child being on the streets, but they do an assessment to decide if you need longer term support with housing and any assessment would see the savings and say that the OP has means to pay for accommodation. At the point, and assuming theres no successful appeal, they'd end the temporary accommodation.

OP it's perfectly legitimate to use savings on housing and then apply for benefits once eligible if that's an option to you. You won't have to run them down completely, you'll still get a decent contribution if you're under 16k.

Have you applied for CMS from your ex?

Unfortunately, that's what you're going to have to do.

The alternative is that you present to the council as homeless, they have a legal obligation to help you as you have a child.

Try Womens Aid. They may be able to get you a referral for social housing or deposit guarantee schemes.

Is there absolutely nothing that you could buy? Might be better than running down savings on rent...

As others have said the reason you're ineligible for benefits is because it's expected that you would use your savings on housing/living costs first. Is it feasible to take on a tenancy and pay until the point your savings are under the threshold and then claim?

It's also worth getting on the local housing register though depends where you are as to how long that would take/whether it's realistic

If your savings make you ineligible for benefits, you must have over £16k.

You would be expected to use this money to secure a home, then submit a claim for Universal Credit when your savings have reduced to less than £16k.

Well done on getting out of the abusive situation you and your child were in. However hard things are at the moment, don't go back!
Is there absolutely no way you can stay at your parents for a little longer- do they realise how tricky this is for you- costs of rent and all the obstacles?
Good advice re speaking with shelter and citizens advice.
I have nothing more to add only I hope you get sorted soon. Good luck

Yes, I think you may well have to use your savings. For instance you could pay the rent in advance by several months - this needs a trustworthy landlord and a place you feel secure with liveable neighbours.
But do get advice as you might be eligible for some kind of help to find somewhere.

Oh, and put your name down for social housing if you haven't already!

One logical approach would be to find a budget, but acceptable flat and run down your savings to meet the rent. Apply for benefits when you reach the threshold.

I second asking Shelter, though.

It might be worth speaking to Shelter. There’s a requirement for local councils to support victims of domestic abuse and they should be able to advise you how to navigate this. That you’re staying with your parents might muddy the waters but I assume they could only help temporarily.