They will get that name cancelled for having false details, if they contact Nominet it will be sorted pretty quickly.
I don't know why he has to send cheques back either, the domain name makes no difference to the bank account name. Your bank account name can be a million miles away from your url.
The Registant may be given an opportunity to amend their record with the Registry before any cancellation occurs.
The article is written in two parts. The first part is relating to the name of the foundation,
[snip]
Well Nominet can (have done before) declined to give anyone to opportunity to rectify the registration. Unless someone can prove they are Mr / Mrs SGHUK by means of a birth certificate or driving license then Nominet don't have to give a person other than who is on the whois the authority to change the details.
They have done it quite a few time where the registrants name is so bizarre that it can be cancelled.
You don't need to register at companies house though to get a bank account, quite a few charities aren't registered at companies house. Up until a few years ago the RSPCA weren't registered at companies house. They tend to only register at companies house because it gives them protection to sue third parties for libel etc. As the law stands (until recently at least) Charities can't sue for damages.
All he has to do is register with the Charities commission and he'd be fine to open up accounts.
I've never operated a charity so unfortunately I cannot comment, except to say I suspected he is expecting significant financial interest so might want it through a company. I've not checked with the Charities commision to see if the name has been taken with them. Perhaps it has.
Domainers getting a bad name again
If you sign up to the group you get a little badge to put on your site, so the public is aware you follow some sort of honesty code as set out on a 'Guild of Domainers' website.