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Hello, this is Jim and welcome to JustAnswer. I will be the lawyer working with you today.Sorry to hear of the issue. I will set out my written answer shortly.
Under the GDPR data law, you do have a right to erasure of your data. However, the data controller (the agency) could claim an exemption if they need the date to ensure compliance with their regulatory requirements including the need to be able to defend a negligence claim or a breach of contract claim. So my view is they would be able to retain the data for up to 6 years as a maximum. You could request they erase the data but I would expect them to come back to you to refuse - their will have an insurer. The insurer will need to pass any potential claim to their solicitors - the solicitors will need the data to be able to defend a civil case against the agency if for example you sued them. That is my understanding from a legal perspective. The Information Commissioner's Office (ICO) handles all things "data".
I would recommend that you speak to the ICO on 0303(###) ###-#### They also have a "live chat" facility on their site - you can visit it here: https://ico.org.uk/make-a-complaint/
I hope this helps and answers the question - my goal is to ensure you are happy with the answer and have the information you need. If you have any follow up questions then please let me know. I will reply as soon as I can to help with any further queries.
Please let me know if the answer helped or if you need me to cover anything else?. I am happy to clarify the answer or if you have any follow up questions. If so, I’d be grateful if you would let me know. I am free most days, including weekends, so feel free to ask me anything you are unsure of.