I dont think you can rely on Hamilton if the claimant has presented the true facts to the DWP, and the DWP has simply come to a diffferent conclusion.
This is because all capital must be disregarded where IS or income based JSA is (lawfuly) in payment
The Court of Appeal held in Mia v SOS 25 July 2003 that if the family are normally occupying both properties as their home, then both should be disregarded as capital as the dwelling ocupied as the home.
Lord Justice Ward summed the issue up thus at para 1 of the judgement:
“The issue.
1. This is the question which arises in this appeal: is there one dwelling or two dwellings occupied as the home where a claimant for jobseeker’s allowance normally occupies as his home two houses separated from each other by other houses in the street, each house being overcrowded if the claimant and his large family were removed from both houses into only one of them? On 23rd May 2002 the Social Security Commissioner, Mr E.A.L. Bano, so construed the Jobseeker’s Allowance Regulations 1996 as to lead him to the conclusion that there could be only one dwelling in those circumstances but he gave the Secretary of State permission to appeal to us.”
The appeal was dismissed.
Maybe your Council may have to register the properties as 1 dwelling for CTX purposes in this case