It doesn't sound like you're familiar with the UK system either. Bail in the UK means adherence to specific conditions, i.e. live somewhere the police can find you, stay away from the victim and don't leave the country. It doesn't involve cash changing hands. If you've done something very bad, or are a big flight risk you will not be granted bail, but again, not a money issue.
The person you're responding to is referencing that sentencing is done by a judge who is supposed to be more objective when determining sentence, as opposed to emotional juries who simply determine if they are guilty or not of accused crimes.
It absolutely is not. It's about risk of absconding. Secondly, no, cash bail is not a thing in the UK. Someone being arrested in the UK for extradition is not part of the UK justice system, they are merely passing through at the request of a foreign nation. Unsurprisingly, foreign nationals can't have their passport taken away by a foreign country, who'd have thought?!?!??!
The person you're responding to is referencing that sentencing is done by a judge who is supposed to be more objective when determining sentence, as opposed to emotional juries who simply determine if they are guilty or not of accused crimes.