Permission still applies to it whether its music or a sound clip as it's still audio. It's a sound clip that you did not record and therefore does not belong to you so you need permission off the copyright holder. For sound clips they use the same system as music with the licensing so it's the same. Sound clips still have Royalty Free music services so whatever was said applies to it. Not too hard to grasp
If they do not state that you have permission to monetize it on their website or if they don't use creative commons licence then you will have to email them so they can send you permission for use but that's up to them then. Also can you link me the website you refer to so I can take a look as I dunno whether it's
this as there are other websites that are titled BBC. If it is the one that I linked then you have permission to use it as you wish as stated by them ("serve as stimulus for a range of other work. It's a flexible learning resource for you to use as you wish") but it is kinda vague statement for someone who plans to use their clips for YouTube and their
FAQ is also vague. I'd email them too to clarify it as there FAQ section does no give enough detail but they do have a contact us section for queries just to be safe. You could argue that their website says that you can use it as you wish so there would be no problem there however the BBC sound library is known for educational uses so just to be safe I'd send them a query.