Britannia Rules blog. The argument is that the House of Lords Act 1999 did not amend the Letters Patent by which peers were appointed. At this stage, I offer the link without further comment other than to say that, if it was to be legally correct, the consquences would be massive.
The creation of a peerage and the law of peerages is complex but most peerages have been created under the Royal Prerogative by issuing Letters Patent- see Bebretts. [Also, FOIA and here].