Yes, the UK has the DPA-2018 legislation which basically implements GDPR in the UK. [1] Its application is supervised by the ICO. Subject Access Request can be issued to pretty much any public institution / company [2]
"You have the right to find out if an organisation is using or storing your personal data. This is called the right of access. You exercise this right by asking for a copy of the data, which is commonly known as making a 'subject access request"