James - when my company was acquired, we had A through E shares which carried different rights - given UK tax, I don't think mutliple share classification structures are unusual. Bear in mind that while the acquiring company wants control and in your case would be initially interested in the 'A' shares, if the 'B' shares carry a right to dividends, then eventually they may wish to acquire those too, as they won't necessarily want to keep paying the 'B' shareholders a share of the acquired company's profits.
Of course, if they are acquiring to get access to certain intellectual property, for example, but there is no likelihood of future profits, then the 'B' shareholders are at risk of being abandoned with their shareholding being effectively worthless. If this might be the case, and you wish to protect the 'B' shareholders interests, then this should be built into the Sale and Purchase agreement.
As with any complicated legal transaction, you are well advised to get a decent lawyer, and to get your company paperwork (articles, shareholders agreement, etc.) in order before you get anywhere near an acquisition process. (Apart from anything, it is a good indicator of a well-run company to any potential acquirer.)