Yes, you can. You need to inform them you have separated and that you are no longer living together as a couple but still need to share your house. They will end your current claim by removing the "partner" who needs to make a separate claim in just their name. You will need to decide who keeps parental responsibility for the children for benefit purposes. If this is you but child benefit is in your partner's name you will need to swap it over or vice versa, they will/should ask for evidence of this such as your Child Benefit award letter. Take a look at your tenancy agreement, I'm assuming you are a tenant rather than owner occ, if it has both names on it is easy enough to split the rent 50/50, if not it gets a bit more complicated but they should tell you exactly what they need in order to pay you both the right amount for housing costs. They shouldn't refuse to accept that you are no longer living together as a couple but they may ask further questions or even set a note to ask you more questions in the future.