Am I allowed to refuse to have a headshot photo taken at work?

They're making us take headshots for the company website and social media. Am I legally able to refuse my employer to take photos of me?

I've checked my contract and there's no mention of me signing away my right for them to be able to have access to my photos for marketing ect.

There are already some photos of me on their social medias from training days and parties. But I don't mind those ones being up as they're group photos. I'm drawing the line at headshots!

How should I refuse? Should I quote The Data Protection Act 1998 or 2018?

Thanks in advance.

Edit. Thanks for all the advice everyone! I wasn't brave enough to say no, so I just had it taken and it wasn't as traumatic as I thought it'd be. I've just asked them to not post it on the website or social media with my name attached as I don't feel comfortable with having my identifiable information publicly visible online. (I don't have any personal social media accounts either)