See below for some examples from the House of Commons Journal Office's Guide to laying papers which suggest that 'covering letter' and 'cover letter' are equally valid (and interchangeable) options in UK English in this type of context:

(...) When laying a paper you need:
two copies of the paper;
two copies of the covering letter (one stapled to the front of each copy of the document) and a third copy of the cover letter to act as a receipt.

The cover letter should state:

the title of the paper;
the authority for laying the paper (e.g. Act, Command);
what or whether any parliamentary procedure (e.g. negative, affirmative) applies;
whether there are any accompanying documents (e.g. explanatory memorandum or impact assessment);
the name of the Minister formally laying the document;
contact details, including a direct telephone number, of the person responsible for laying the paper; and
(if applicable) that the document is being laid in proof or ‘typescript’ form. A “proof” copy for laying must be correct and not different in any way from the final published version.

Sample cover letters are available at Appendices 3 and 4.

Appendix 3:
Sample covering letter for an HC paper, Act paper or Command paper

Appendix 4:
Sample covering letter for a Statutory Instrument
https://www.parliament.uk/documents/upload/laying-papers.pdf

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Note added at 1 day 12 hrs (2018-07-22 21:26:59 GMT)
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PS. Reference comment provided based on the fact that 'oplegbrief' is typically also used in the context of laying papers before parliament.

oplegbrief

cover letter , covering letter , accompanying letter , accompanying note , submission letter

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Note added at 11 hrs (2018-07-21 21:21:52 GMT)
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UK and US use cover letter. It's not a US/UK divide

What Is a Cover Letter | Monster.co.uk
https://www.monster.co.uk/career-advice/.../have-a-cv-why-do...
A cover letter is a great addition to a CV when applying for jobs and can make ... Ideally, a covering email will make a brief introduction and mention your CV has ...

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Note added at 1 day 2 hrs (2018-07-22 12:22:13 GMT)
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Three excellent cover letter examples | Guardian Careers | The Guardian
https://www.theguardian.com/careers/covering-letter-examples
Feb 11, 2014 - Cover letters are the first chance you have to impress an employer – they're not just a protective jacket for your CV. Here's our guide on what to ...
You visited this page on 7/21/18.
Your complete guide to writing a cover letter for 2018 | CV-Library
https://www.cv-library.co.uk/career.../cover-letters/how-to-...
Jan 3, 2018 - Cover letter tips: Write the perfect cover letter for your job application. ... email addresses like [email protected] won't make you ...
Cover letters | Prospects.ac.uk
https://www.prospects.ac.uk/careers-advice/cvs-and-cover-let...
To give your job application the best possible chance of success you need to know how to write a relevant and concise cover letter. Take a look at our example
Cover Letters - Aston University
www.aston.ac.uk/careers/cv/cover-letters/
A cover letter (or covering letter) is often overlooked by applicants as less important than other parts of the application, but in fact it's a vital part of your sales pitch ...

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Note added at 1 day 13 hrs (2018-07-22 23:13:27 GMT) Post-grading
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