OK, since I'm unable to sleep, I've done some more digging and found this on benefitsnow.co.uk:
  "The criteria for living alone is that there are no non-dependants aged 18 or over who normally reside with you or who you reside with. A non-dependent is usually one of your adult children who lives with you.  
The following are not classed as non-dependents and will therefore be ignored when awarding severe disability premium;
 
 a person who lives with you and makes payment to either you or your landlord for rent"   (my emphasis) 
 Full list here: 
www.benefitsnow.co.uk/jsa/incomebased.asp  If this site is correct, I think - hope! - I should be OK.  I'm still getting advice tomorrow though.