Solution 1:

"Prisencolinensinainciusol" is a song by the Italian singer/comedian Adriano Celentano with nonsense lyrics that are intended to sound like American-accented English. As it happens, I played it for my wife two nights ago and asked her to guess what language it was sung in; she eventually guessed English, though she couldn't understand the words. So if it's convincing enough to fool my wife, a native English speaker, I'm happy to accept that it's a pretty good simulation of what English sounds like to non-English speakers, or at least to Italians. Celentano apparently speaks no English himself, so it's a "pure" simulation, untainted by any actual knowledge of the language on the part of the singer.

You can see and hear "Prisencolinensinainciusol" here, and listen to an entertaining NPR radio story about it here. Warning: this song is incredibly addicting.

Solution 2:

So far as I'm concerned, the acknowledged master of of the art was Stanley Unwin, whose "gibberish language" is sometimes called Unwinese. Here's an example on YouTube...

The bizarre thing about Unwinese is that although it's probably incomprehensible to most non-native speakers, Anglophones normally find it relatively easy to get the gist, because it has the exact cadence of normal spoken English (and the odd semantically significant morpheme).

Solution 3:

Here's a video of some "English" gibberish - https://www.youtube.com/watch?v=Vt4Dfa4fOEY

Solution 4:

Lewis Carrol's Jabberwocky is a famous example of grammatically correct English gibberish.

I guess it does not entirely count as gibberish because the underlying structure is correct, and there are many actual English words in between. Many of the descriptors of the poem call it nonsense rather than gibberish.

So, whether or not you consider it According to Hoyle gibberish, I think it deserves honorable mention. If for no other reason than the common adoption of many of its neologisms! (e.g. galumphing, and chortle.)

Solution 5:

The only examples I can think of are of English comedians into other languages -

The best example is Catherine Tate's 'offensive translator' sketch, which you may know, but if not, enjoy! (apologies if it offends anyone)

Check out Kenneth Williams's accents clip here.

His 'Ma Crepe Suzette' isn't gibberish, but I'm including it for variety.

ADDITIONALLY:

I've done theatre impro courses with Keith Johnstone and he uses 'foreign gibberish' cards to help weak/unconfident improvisers find their way into impro. There may be some references to his methods in his 2 books on impro.