I think there's a couple of options, none fitting perfectly. First, for a one-word close synonym I think of the verb:
- Moonlighting
- Defined by M-W as an intransitive verb meaning "to hold a second job in addition to a regular one".
Secondly, due to my legal background as an American lawyer, your example of using company equipment for your own activities makes me think of the legal term of art
2) "a frolic and detour"
-So, at least in America if you use company equipment for activities OUTSIDE the scope of your employment and without the companies consent, you are going to be on the hook for any damages you cause if you're negligent and injure someone and also might be fired. (I say this because of the Urban dictionary definition stating: "doing Foreigners is a fairly accepted part of British working life and, depending on the workplace, can even be done with managemental consent")
So, for example let's say you get in a car wreck driving the company car home on your commute from work while, and your job policy states that employees like you can only use the company vehicle for 1) company travel, 2) family-related activities (such as school pickup of children, medical care, etc.) , 3) to go to the gas station, or 4) to get groceries. I would venture that so long as you were driving merely negligently, not with gross negligence or "reckless disregard for human life" or intentionally hit someone with your vehicle, your Employer is going to be on the hook for damages not just you in all likelhood.
On the other hand, if you let's say crash your company car at a strip club on a Saturday night, a victim likely wouldn't be able to recover from your Employer due to the common law principle of respondeat superior (Latin for: "the master must answer" (for the reasonably foreseeable mistakes of his servants), despite the accident involving your with your Employer's car. Thus, in this scenario where your "frolic and detour" with the company car wasn't in the scope of your employment or reasonably foreseeable, your Employer likely wouldn't be jointly and severally liable to the victim under the legal concept of respondeat superior and therefore on the hook for payment of damages. Rather just you, the tortfeasor, could be found to be "personally" liable to the victim, which isn't as good for the victim because you don't have "as deep as pockets" as the huge company that employs you. A company since it's a "juridical person" (i.e. a non-human legal entity) and not a "natural person" would be vicariously liable only through the actions of its officers and never personally liable. Sorry for getting into American tort and employment law concepts too much, but it seemed à propos.
An American HR person would tell you it's a "misuse of company resources" unless it's within the scope of your employment or OK'ed by the proper party.
- Lastly I think of the phrase: doing something "off-the-books"
- M-W defines "off-the-books" as: "not reported or recorded". And you'd definitely be doing "something off-the-books" if it's with company resources/on their property but not within the scope of your general employment or something you have implicit, written, or verbal consent for.
In sum, as your internet lawyer, be careful "doing a foreigner" because you might end up getting fired for that foreigner you did if it's not with your work's consent (and something goes wrong!)
Lastly:
As an aside, is there a word which means the misunderstanding of two phrases that sound identical but have completely different meanings?
Yes, that's a "homonym", or if you want to split even more hairs there are "homophones" and "homographs", homophones sound the same but are spelled differently like "there" and "their", and homographs are words that are spelled the same but have different meanings like "lead" (the metal) and "lead" like to lead others.
However, here I would call this phrase an "idiom": which M-W defines: "as an expression in the usage of a language that is peculiar to itself either in having a meaning that cannot be derived from the conjoined meanings of its elements."
Interesting question, I like learning strange British expressions I would never otherwise hear as a Yankee!