Some context, for those less familiar with the BBC: that piece is the script for A Point of View, a short Radio 4 programme in which the presenter (changing every few months) offers their thoughts on a topical issue, with the emphasis on providing entertainment. As such, it isn't intended to be a serious examination of the issues surrounding attempts to deal with ageing.
It might be worth people responding in the comments, as head-grafting and extending decrepitude are both harmful misrepresentations of what people engaged in this type of activity are trying to achieve.
Ah, didn't realise it was a radio program. That explains the rambling nature of it, when speaking it's more generally acceptable to ramble than it is in writing.
The BBC News recently ran an interesting piece on living forever. They discuss some of the standard arguments against cryonics and transhumanism; overall, the article is pretty critical of both. I suspect most LessWrong readers won't find it convincing, but it's still worth a quick read.