Joint mortgage UK, what if I leave?

We've had a joint mortgage for about 18 months.
If I leave the house, how do I come off the mortgage so my boyfriend can put it in his name solely (e.g. Do I just tell the lender I've moved out)?
I have no working income at the moment so myself and my child would have to claim benefits to get a home initially, I'm not sure if I can get help with rent if I 'own' a home.

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