To be clear, the Co-op isn't going to withdraw from banking tomorrow, so there is no reason for Co-op depositors to feel they are going to belefthighanddry.
The reason the billionaire oligarchs feel it is a legitimate fear that they could belefthighanddry is because it will take many months for them to sell their stake: the sale would require regulatory approval and also the unwinding of the complex network of international companies through which they own their stake in TNK-BP.