Board Directors must by law participate fully in Board discussions.
You have to “exercise Independent Judgement” under s173 of the CA2006 (Companies Act).
You must also “exercise Reasonable Care, Skill and Diligence”, under s174 of the CA2006.
You can only fulfil your S173 and s174 duties, if you pay proper attention to the subject being discussed and understand the subject; at least to the level necessary to be able to take part and form meaningful judgements.
It is illegal to do otherwise and would be a serious breach of your duties as a director.
If your lack of genuine participation in Board discussions were to lead to an obviously bad Board decision, that in turn could be argued, caused or contributed to the collapse of the company.
It could be argued that your negligence was so severe that it constituted gross negligence.
In that case creditors who lost money, could argue that their losses were at least in part due to your gross negligence and therefore you should personally compensate them, at least in part.
That would allow them to raise the corporate veil to partially set aside the normal limited liability protection.
The key message here is you cannot “tune out”, whilst others discuss the (boring?) annual financial statements. You must “exercise Independent Judgement”. It would be illegal, to vote yes, simply because the FD does.