Yes. Data protection law gives you the right to know the type of personal information your employer holds about you, why that information is being held, how the information is being used or will be used, and who will be able to access that information. This is known as a data subject access request. There is information on the website of the Information Commissioner explaining how to make a request.
You can write to your employer, asking for a copy of the personal information held about you, provided this is held either on a computerised system, or is held on paper and is organised into a 'relevant filing system' (in other words, is held in a structured filing system, so that the information about you is easily located).
Organisations used to be allowed to charge you (up to a maximum of £10), but in May 2018, this right to charge was abolished by the General Data Protection Regulation (GDPR). Now an organisation can only charge for a subject access request that is “manifestly unfounded or excessive”.
Your employer must provide the information you ask for within a month. Requests can be refused if they are ‘manifestly unfounded or excessive’, but if your request is refused, your employer must tell you why, and must inform you of your right to complain to the Information Commissioner.
When responding to your request, your employer must first use “reasonable means” to check that you are who you say you are.
To avoid an objection by your employer on the basis that complying with your request is unfounded or excessive, it is sensible to make sure it is as clear, simple and narrow as possible.
You can also ask your employer to correct, delete or destroy any personal information held about you that is factually incorrect. This could be especially important in relation to disciplinary records or information about your health.