It's called a compromise agreement and is a valid way to pay financial compensation to someone to leave a role without pursuing a misconduct or redundancy option.
You can negotiate the amount and £10,000 may have been a starting offer, however if the company is prepared to pay then you are entitled to ensure the agreement includes clauses such as a recognised reference wording and you can choose how it is communicated why you have left. You also have to be given independent legal advice.
You leave with a clean record and with money in your pocket with confidentiality for both sides.
Also the fact that a compromise agreement has been discussed can't be used against either side in the main part. Therefore not blackmail at all, but still not nice if you weren't expecting it.