Q:

Can I resign if given a "second chance" (UK)?

I broke my contract. I had a meeting with my boss where at the start of the meeting he intended to terminate me immediately. At the end of the meeting he decided to suspend me for two days and bring me back for another meeting.
The next day I emailed him (while suspended) accepting responsibility and accepting the termination.
The following day I went in for the meeting and he essentially said he was considering giving me a second chance and asked whether I really wanted to leave or if I just thought it was "the right thing to do". I said I'd have to think about it, and he prolonged the (paid) suspension by another week (which is currently ongoing), and arranged another meeting.
I still want to leave. If they offer me a "second chance", and I don't take it, do I have any right to resign, or can I still be terminated immediately for the original offence?
This is in the UK.

A:

he intended to terminate me immediately

So he didn't terminate your contract therefore still in contract with said employer.
This means that they cannot stop you from resigning whether you're getting a "second chance", or you're suspended you are well within your rights to leave within the UK.
Simply approach said boss and state

I've had a think about your offer and I've decided that I do indeed want to leave, thank you for considering me for a second chance.

Your boss clearly knows this as he stated

are you sure you wanted to leave?

Meaning he needs you and is also aware that you are within your rights to leave.

