You can apply to be assessed as a single person. You will need to complete forms regarding the status of your relationship/household and a specialist will assess whether you are deemed to be single for social security purposes. There at a number of factors looked at - sexual relationship, finances, societal perception (do others know you're no longer together etc?)
If that's the case then no, you won't be able to qualify. People need to know you're not together, there needs to be clear proof of that; friends and family knowing, financial proof of independence etc. It's tricky to navigate.
You will need 2 people from memory to be referee's. These people actually need to sign something to say they know you're separated.
My ex & I did it years ago while we looked for separate accommodation. After a certain amount of time they told us we'd either have to partner on the system again, or move out separately. It might've been around 3 months. That was enough for him to finally get out of the house. He was never too interested in supporting his 'family'. Didn't last long though :/
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