Could I submit freedom of information request to my ISP and be provided with all the details they store about my internet browsing? Unfortunately BT are a private company so sounds unlikely..
However, you don't want that: you want a subject access request. This covers data from private sector companies too. Not responding is illegal and you can take them to the Information Commissioner and eventually the Information Tribunal.
This is the information commissioner's office's guide to making a request:
https://ico.org.uk/your-data-matters/your-right-to-get-copie...
Source: trained as a journalist and am quite good at media law stuff. Not a lawyer, but have had substantial training and think this is worth a punt.