The accounts generally aren't linked together. Everything about the UK government IT is a huge group of independent systems all pretty much isolated from each other. You can argue over whether that's down to incompetence, organisational turf wars, or good security design.

Which is why you have completely separate account to pay the same government for crossing one specific brige in East London than you do for vehicle tax.

Most government websites do use the same frontend toolkit (a rare win for UK governmental IT) but front completely separate systems.