How long is a piece of string?
What seems to happen is that one set of vested interests in the USA calls in a favour that their financial backing of politicians elections bought they (at least their politicians are honest: once bought, they stay bought) and "remind" said
puppet lawmaker about all the goodness they've received - and now it's time for the quid pro quo.
Since the politician has nothing to gain from standing up for the little guy - he's a brit, so will never vote for an american politician - and a lot to lose from annoying his paymasters, so the extradition is demanded. The puppet strings are therefore extended across the Atlantic and the american government asks (a word that loses a lot in translation - "demands" is closer) for the warrant to be executed.
Again, the british Home Secretary has nothing to gain from annoying his/her/its puppet-master and a lot to lose from incurring their ire. So the form gets stamped and "justice" is done.
A guy gets shipped off to a foreign country. One where he cannot raise any sort of defence as the costs of flying witnesses over (at his expense), accommodating them until the trial calls them (again, he pays) and paying for an american defence team is crippling - even for british millionaires who've been shafted by this form of "justice". Hence he does what almost everyone else in his position does: makes a deal. Not only does that prove, in the eyes of their law, that he's guilty but it also justifies back to the HomSec that he/she/it was right in approving the extradition - "look, he pled guilty!"
In fact all that's happened is a commercial interest in one country has pulled the strings of a tame politician, who has yanked the chain of an emasculated and disinterested british minister. The level playing field of law then gets tilted massively in favour of the company and the defendant has no choice but to roll over, thus completing the circle and proving to all involved that the system works.