This answer is meant to supplement the answer by user6726 and to follow up to your comment that "it seems the world upside down, somebody uses another's identity to sign up for a service and it's the latter who must be careful not to be a criminal."
The situation might not seem so unreasonable if we consider the effect of the GDPR (and possibly similar laws elsewhere). The GDPR applies to sites (data "controllers" in the GDPR terminology) which are based in EU member states, the UK (in a slightly modified form known as the UK GDPR), and to controllers outside the EU/UK if the site offers goods/services to data subjects who are in the EU/UK, pursuant to Article 3.
In order to process personal data, the controller must have one of the 6 lawful bases for doing so. The lawful bases are (1) consent, (2) necessity for performance of a contract with the data subject, (3) compliance with a legal obligation, (4) necessity to protect a vital interest of a person, (5) necessity for the public interest or official authority, and (6) necessity for the site's legitimate interests (Article 6).
It should be quite clear that none of those would permit a normal online service to process your personal data in this scenario. They do not have your consent, they are not in a contract with you, and there are no legal obligations, vital interests, public interest, or legitimate interests for keeping that data.
Where a controller has no lawful basis for the data processing, you have the right to erasure. Article 17 provides:
- The data subject shall have the right to obtain from the controller the erasure of personal data concerning him or her without undue delay
and the controller shall have the obligation to erase personal data
without undue delay where one of the following grounds applies: [...]
(d) the personal data have been unlawfully processed;
Article 12 provides more information on exercising your rights against controllers (including the right to erasure).
So, in your scenario, although you may have no right to access or delete the account which does not belong to you, you may have the right to require your email address to be removed from it. Going back to your comment, this seems quite a reasonable scenario: your rights extend to the aspects which affect you but not to those which do not.