To take each part of the statement / question in order...
Taking the detail of attendance as presented at face value and that no apologies have been offered / accepted by the council, the vacation of office by failure to attend meetings isn't 'enforced' by any action of the council or the electoral registration office.
It is rather 'enacted' by virtue of LGA 1972 s85 (1):
Subject to subsections (2) and (3) below, if a member of a local authority fails throughout a period of six consecutive months from the date of his last attendance to attend any meeting of the authority, he shall, unless the failure was due to some reason approved by the authority before the expiry of that period, cease to be a member of the authority.
So, technically, the only 'action' is that of non attendance and that is the 'action' which determines vacation of office as a Cllr.
The 'administration' is more localised - for example, the clerk, if there is one, would normally be expected to inform the electoral registrations office of a casual vacancy. If no clerk a Cllr so delegated might do this. It might also be appropriate for the council chair (or clerk) to include the fact that a casual vacancy has arisen at the next council meeting.
Whether anybody needs to inform the individual that they have vacated their office is also a localised decision.
It is the Act which 'enforces' the vacation of office following the failure to attend by the individual.
It could be argued that a person approaching the 6 month period might be reminded of the situation but if they are habitually non-attending and ignorant of the consequences, perhaps they should take charge of their own destiny...