A simpler explanation of how to do it ...
1. A trust is made a member, with a block vote. (I suggest a trust since they have the advantage of low running cost). It is owned or entrusted by Wikimedia UK. It runs a specific commercial side of Wikimedia UK: recognising certain "anonymous editors" as people it will legally represent as a member, in return for a once-off payment, with all "profit" passing to the foundation. It identifies these editors via a nom de plume, a wiki* email, or any other means of identification that's verifiable and not a real name (eg, a password or similar) rather than storing "real life" ID. Criteria for appointment are roughly at a parity to the criteria for membership (this prevents abuse via carpetbagging).
2. There is a once-off fee for the benefits, namely lifetime representation within the trust's membership rights (roughly at a parity to the membership fee, plus a couple of pounds perhaps for admin costs and because they are not liable under the £1 guarantee as members would be.) In return for paying this once-off fee, the trust provides a lifelong representation service - it allows them one vote of its block vote, attending rights as a "representative" and the like, so that people who pay via this route can effectively exercise the same rights as Wikimedia UK members.
3. The system if done right is not susceptible to abuse. Only people who meet similar criteria as members would have to can become clients of this trust (or company); they must pay a similar fee to that payable by members (including an amount equivalent to the £1 guarantee); they gain in return the rights which Wikimedia UK members have of effectively, speaking, one vote, notification of legal matters, and attending meetings, and the system is immune to people gaining more rights, or having a say within Wikimedia UK, or multiple vote stacking or rigging, identically as if they had joined Wikimedia UK directly as members.
4. However as they are clients of a commercial (non-profit making) operation, and are paying in order to get a service, they are neither in any legal arrangement or contract with Wikimedia UK and cannot be ID'ed from that side. Nor are they trustees, or officers of the commercial body. They are clients pure and simple, and in a contract with the trust (or company). The law is that client transactions must be recorded for commercial bodies, but no law states that personal information must be, and provided Wikimedia UK is happy with the new joiner, no details of personal name need ever be on file. Recording pseudonyms, dates, and that a Wikimedia UK officer has confirmed the person has met the same criteria as for membership, is sufficient.
5. The surpluses of these once-off fees are then passed to Wikimedia UK as charitable donations or distributions, keeping the commercial arm profit neutral and free of tax, exactly as for the commercial arms of all other charities, foundations, and trusts. This parallels the £20 or so membership fee which non-anonymous members would have to pay.
Hope that makes sense. Legally this (or something like it) is watertight under UK law, and would cost almost nothing to run. Perhaps if it did cause extra cost, charging people who wished to be anonymous members via such a scheme a small extra sum to cover the extra running costs, would not be seen as unreasonable. But it shouldn't.