I have just offered a young Polish player in his 4th year at the club. A regular in the Polish under 21 team . been in the UK for years, How can he be refused a work permit ?
He has lived here for years. Your programmer got this wrong.

sign him anyway

Not necessarily. It's longer than 4 years to become a British citizen. And, therefor normal rules apply.
There's a number of things that give the player points. Pay, first team appearances, national caps etc.
Being in the under 21s doesn't mean they're guaranteed to get a WP.
There should be an indication if it's likely.

1. It takes 10 years for a player to be able to apply for work permit
2. Your player is ♥♥♥♥