To whom it may concern (if you can find a name through LinkedIn or the company’s website, even better!),
I appreciate interns can sometimes be difficult to fit into a busy team and aren’t always considered a priority.
If offered an opportunity I would be as useful and focused as I could be when needed and happy to read and learn when the team do not have time to involve me. I am great at researching and note-taking and would willingly turn my hand to any task in return for the opportunity of learning about your business and its operations.
I am committed to pursuing a career in X industry and your company stands out as an exciting employer within that environment.
I have learned much throughout my (list course/education/experience), I have (list accomplishments/evidence passion for the role, ie, I have recently taken part in Springpod's Law virtual work experience where I particularly enjoyed…).
I understand that you have a formal recruitment process, but if you are currently experiencing a high workflow then I’d like to be of assistance. My CV is attached.
I am available to start from (date) and would appreciate any opportunity within your team.
Thank you for your time and I look forward to hearing from you.