The articles in place for the said company are silent on the matter
Well, it's a highly sensitive matter and should definitely not be talked about on a public forum.
Directors' resolution will do.
I am not aware of a need , CA2006 s392 merely says a company may by notice to registrar specify a new accounting reference date, I believe the setting of it is therefore in the hands of the directors (subject of course to exclusions re S 392(3) re frequency of change.
So a board minute would likely be fine, do not think it needs to really be sent anywhere (except possibly the bank if borrowing their money)
Well clearly the directors need to decide to make the change. How, if at all, they wish to record the decision they have taken is an internal matter.