Joint claim to two single claims

I have a client who is currently claiming Income Support as a couple with the person they share their house with.  They say that they are not a couple and never have been, but that the Jobcentre advised them many years ago to put in a joint claim as it would be simpler than proving they are not living together as husband and wife.

As they are now hit by the bedroom tax, they want to change this to two single claims. 

My concern is that once the two single claims go in, it will take some time for the LTAHW issue to be investigated, and that they could be left without any income.

What would be the best way to handle the transition?

Thanks

On what basis are they claiming IS? Would they both be entitled to single claims?

She’s getting carer’s allowance, so could claim IS

He’s getting DLA, and should be entitled to ESA