You don't have a board of shareholders - you have a board of directors. All shareholders are entitled to vote (providing the class of shares they own allows them to).
Board minutes are from board meetings involving directors. At a general meeting with shareholders, you have general meeting minutes.
If a company is planning to buy another company then yes the board of directors can agree to purchase it. However, the company being sold, the target, its shareholders will need to agree to sell their shares and as I mentioned if the target's board recommends the offer then it is recommended if not its a hostile takeover where the shareholders go ahead and sell anyway.
Sorry Ricky but that's not quite right (or we may be talking cross purposes!)
Private Company Sale
If company A is buying company B from company C then the following occurs:
(1) Company A board minutes to approve the purchase
(2) Company B
board minutes to agree to register Company A as the new holder of shares in Company B (plus any miscellaneous items like director apptments / resignations)
(3) Company C board minutes to approve the sale
You only need shareholder general meeting minutes for items prescribed by the CA 2006. The target company (B) has no say in whether it's sold or not - that's up to Company C (and in turn by the board of directors of Company C).
Public Company Sale
This is essentially the same structure the above, except that the individual public shareholders are the equivalent of Company C (not B). You are right that these shareholders need to agree to sell their shares and this is indeed by a vote at a general meeting of the shareholders. Whether or not the board of directors of B recommends the sale will determine if the deal is recommended or hostile. (EDIT: and you only need to worry about recommended / hostile deals if the target (B) is publicly traded. There is no such thing as a "hostile" private sale.)
Deals with public elements may also require shareholder approval per the Listing Rules/Takeover Code but these are less common.
The general point remains that in a private M&A sale there is no shareholder approval required.
Hope this helps!