At first glance SSDI is broadly similar to DLA etc. however the devil is in the details in as much as how the Government defines " ...match the following UK benefits". I am no expert here and I don't believe HMRC are clear either.
There are various ways certain benefits are qualified e.g. residential, contributions, which may impact their inclusion/exclusion.
I have also phoned them and got put through to a "technical adviser", a step beyond the regular customer service bod., who took relevant details and promised to call back within a week, this was 3 weeks ago, nothing yet.