As i understand it:
In EU/EEA there are are bank regulations specifying that banks may operate on a common market under supervision of regulating body where the bank is registered. As Landsbanki UK was branch office and not subsidiary company, it falled under Iceland regulation.
These regulations also require that there is a deposit guarantee scheme for protection of depositors up to 100k EUR, based on country where bank is registered.
So when Landsbanki crashed, all its depositors were entitled to deposit guarantee from Iceland deposit guarantee scheme. But this system cannot handle crash of such size. After that, Iceland government decided to reimburse icelandic depositors, but not offshore depositors (although both have the same claims after icelanding deposit guarantee system, the local ones have political power).
To avoid political windfall, UK (and AFAIK also Dutch) government decides to reimburse their local depositors and get reparation from Iceland based on Iceland government's failure of setup proper deposit guarantee scheme / sufficient regulation, which was condition for allowing its banks access to UK/EU banking market.