This article states that the UK doesn't have the numbers they would struggle providing 10,000
"I mean, if we were to deploy 10,000 troops, each rotation for six months, that would effectively tie up 30,000 or 40,000 troops and we just haven't got that number available.
As of October 2024, there were 74,612 members of the UK's regular Army forces (excluding Gurkhas and volunteers), according to the latest Ministry of Defence (MoD) figures.
https://www.bbc.com/news/articles/czep44jn9jyo
The only way of getting anything close to 100,000 troops would be to bring in conscription
but how many people would be signing up opposed to leaving the country is anyone's guess