Hi Cfergie
I am not 100% certain if the rules in England apply to Scotland but fellow mods will put me right if I am wrong.
If you move to a different local authority and you need to claim Housing Benefit, then your friend will need to claim UC. If they don't need to claim help towards their rent then they can stay on IR ESA. If they receive CB ESA then it will make no difference, they just need to report a change of address.
When ever you are talking to an adviser about ESA, you need to tell them which type(s) of ESA they are claiming, at present there are 3 types; IR ESA, CB ESA and NS ESA.
Prior to January this year, any claimant in receipt of a SDP would be exempt from claiming UC, but this is no longer the case, which has caused upset to many claimants.
Gary
Nothing on this board constitutes legal advice - always consult a professional about specific problems 
