What do I do? Lost my job and my boyfriend broke up with me

I (24,F) just lost my job on Friday over no control of my own. I have been experiencing relationship problems (which I do know are my fault ultimately) where I was unfaithful on one occasion. The person I was unfaithful with was a work colleague and I cut connections and communications until Tuesday evening where a load of coworkers asked what happened. I responded to all and one of the people was the guy, I vented and nothing sinister went on just explaining I had been dismissed. My ex-boyfriend (24, M) and I were already on the rocks and understandably he broke up with me for this. He was going to support me until I found a new job. Now I’m faced with unemployment and no support. My family live across the world. My sister is going through her own thing. I have no friends in my city. I live in the UK so thought I’d apply for Jobseeker’s Allowance and benefits to tide me over as we have a 2 bedroom but my ex won’t let me as it would be seen as a joint claim. All hes offered is either use my savings or hed cover the rent. Job market is rough so I don’t know if I want to use my savings for this. I also don’t feel comfortable accepting money from him as some sort of charity case if we’re not together, I feel like I’m having my last shred of dignity taken away (which is rich from me as I created this situation). Only other option is to move all the way back home with my parents in Asia. Which I don’t really want to do. But I have no options, don’t have friends or family to stay with (my sister & only friend lives witn their boyf family in another city), I don’t want to be reliant on my ex to cover me in the same flat, no landlord is going to rent to me with no job and I don’t want to use my limited savings as I’m uncertain witn the job market. I feel like my back is against the wall to move back home. The move will be expensive so I won’t be moving back to the UK for a good few years. We also share two cats together that I raised from kittens that I’m upset about leaving behind.