The BBC link is a 404 for me. The statewatch one was amusing, in a way, to read someone complaining about how terrible it is not to respect double jeopardy protection ... protection the US has written into their constitution, but has just been torn up over here for the sake of political capital - meaning extradition to the US would give greater protection of that right than facing a UK court! Their complaint about implementation by statutory instrument is almost comically exaggerated too, considering how much UK legislation comes into force by that route - including, as I recall, the extradition arrangements to most other countries...
Yes, some of the politicians talk about a 'rethink' ... but they voted against actually even reviewing it back in 2009, and when the review was eventually carried out it found precisely the opposite of what you believe. Maybe one day they will even change something - but I can hardly imagine they would even attempt to sabotage extradition to the extent it no longer works in the case of a self-confessed criminal facing the prospect of a fair trial, right to appeal then, if convicted of the crimes he admitted to previously, a return to serve the rest of his sentence in the UK anyway.
The key question, though: if, as claimed, the process really is "too quick" and doesn't provide "enough" scrutiny ... why is McKinnon still in the UK now, a full decade after the crimes in question, having spent longer dragging this through every court in the land than the sentence he'd have faced in the first place if he hadn't opted for delaying tactics? If you seriously believe that travesty is "too quick", what would you prefer ... a full decade? Twenty years? Wait until everyone involved has retired and let historians rather than lawyers handle it?