Chartered Secretary here (but not in the UK), FCIS, see posting name ;-)
Anyway, it's 'unusual' (save for mutual investment entities, which enjoy their own body of law) for companies incorporated by guarantee to give members preferential voting rights (which would constitute an apportionment of interests), as this seems to do, awarding votes based on registrations. The Members of guarantee companies have joint and several liability on insolvency, so an unequal distribution of voting rights would seem inequitable on its face.
Further, the notion of a superior interest by one or more members is generally foreign to any charitable undertaking, although a class of members may have super-majority rights (usually constructed to give big donors the right to veto a change of purpose or a substantial distribution of assets). However, I am given to understand that all members are of the same class.
Finally, it may be that it is expressly prohibited, see Ch1, S5 SS3 of the Companies Act 2006 below:
"5 Companies limited by guarantee and having share capital
(1) A company cannot be formed as, or become, a company limited by guarantee
with a share capital.
(2) Provision to this effect has been in force—
(a) in Great Britain since 22nd December 1980, and
(b) in Northern Ireland since 1st July 1983.
(3) Any provision in the constitution of a company limited by guarantee that
purports to divide the company’s undertaking into shares or interests is a
provision for a share capital.
This applies whether or not the nominal value or number of the shares or
interests is specified by the provision."
The behaviour of the Company Secretary is most unusual, and indeed suspicious. Generally, in the event of a members' meeting (AGM or EGM) the Directors set a 'record date' some days prior to the meeting to allow certainty when tabulating eligible members and to declare who is and who is not a member for the purpose of voting at the meeting. This should comprise a formal board resolution and the date should be publicized. Unless the bye-laws of the company expressly permit the suppression of information about voting rights (which in itself would be highly unusual), I do not think that the stand taken by Nominet's Company Secretary and Board would prevail in court, this is, after all, one of the reasons registers of Members are public documents.
Anybody got a copy of the Articles? I'd love to have a look.
I'll have a further plow through the Companies Act, but at first glance, there would appear to be multiple grounds for a legal challenge just on the face of what's been disclosed in this article. I'm pretty sure a court would allow an independent audit of the vote calculation just based on the seemingly furtive and highly unusual behaviour of the executive to this point.