It's not clear from your question exactly what you mean by 'register'. We have a free press so (subject to the usual laws on defamation, etc) anyone is free to publish whatever they want, with no need to 'register' their publications with any governing body (because no such body exists anyway).
However the law on 'Legal Deposit' requires you to send a copy of every issue of your magazine to the British Library and, if requested, also to the National Library of Scotland, the National Library of Wales, the Bodleian Libraries in Oxford, the University Library in Cambridge, and the Library of Trinity College, Dublin:
http://www.bl.uk/aboutus/legaldeposit/index.html
Chris