The paper from The Esme'e Fairbairn Charitable Trust is just that, a discussion paper, it is not therefore the law but one possible interpretation of it.
The Vienna Convention on State Succession in Respect of Treaties is a UN convention, not that of the EU, whose opening line states: "Considering the profound transformation of the international community brought about by the decolonization process".
I'm no expert on international law, but that statement doesn't quite fit the British model of former sovereign states who, having entered into a political union via treaties enacted by each other's legislature in order to create a single sovereign state, enact further legislation to dissolve that single state and revert instead to two.