Is it commonly accepted using the slash to mean "as well as", rather than "or"?
In §6.104, "Slashes to signify alternatives," the Chicago Manual of Style says:
A slash most commonly signifies alternatives. In certain contexts it is a convenient (if somewhat informal) shorthand for or. It is also used for alternative spellings or names. Where one or more of the terms separated by slashes is an open compound, a space before and after the slash can be helpful.
- he/she
- his/her
- and/or
- Hercules/Heracles
- Margaret/Meg/Maggie
- World War I / First World War
Occasionally a slash can signify and—though still usually conveying a sense of alternatives.
- an insertion/deletion mutation
- an MD/PhD program
- a Jekyll/Hyde personality
I read the OP's sentence to mean "US and UK support" -- although it should be noted that its use appears in a comment to the BBC article, and as such can't be considered standard (i.e. professionally produced and edited) writing.
As its use in this case lacks the sense of "conveying alternatives," I can endorse the OP's suggestion to use "US-UK support" instead. However, using a slash to mean and is unambiguous to me, and I personally wouldn't quibble about its use here not conveying a choice between the US and the UK.
On the West Coast of the US, the slash has always indicated an "'and' or 'or'" statement in my experience. When dealing with people from the East Coast however, I've seen it used more commonly as an 'or' statement.
In regards to my experience, I would assume it's entirely regional.