Benefit cap and single claimants

I went to a Welfare Forum recently where it was suggested that there should be few single claimants affected by the cap as a result of the one bed LHA cap already introduced and the exemptions for those in receipt of DLA, which would mean most single claimants benefits were below the cap level. However won’t those single claimants claiming LHA and living in larger private rented properties as have non-dependants living with them, be affected?

For example I have a client who lives with her two adult children who are full time students and her non-dependants, she is currently in receipt of the three bed rate of LHA which is £340 a week as its a central london property. Would she not be considered as a single claimant as her adult children are not considered as part of the household for overall beneift cap purposes? therefore the cap will be imposed and she will have little left once she has paid her rent.

I had a similar client, she had parental responsibility for her two teenage brothers who were soon to become non-dependents and she was living in a 3-bedroom flat with rent of £340. As far as I could tell she would be affected by the benefit cap to her income of £71 JSA + £340 HB, leaving her with £10 a week to live on.