I was thinking about this earlier and we know from the podcast that mimble whimble is a spell seen later in the books to stop an opponent using magic against you. What if during an argument with James, Vernon upset him so much that he went to hex Vernon? We know James has a bit of a temper and with Lily there could she have used it to stop him? On Pottermore it mentions them arguing at Vernon and Petunia's wedding and Lily crying over it so she didn't want them to fight.
Could Vernon have been remembering a moment like that and feel so threatened he thought it might work if he said it?

I never got the impression that Vernon had any idea what he was saying. It is obviously plausible that he actually said the phrase "Mimblewimble" subconsciously, perhaps having heard it through his magical relations. But I don't think for a second he had any idea that this was a spell. I always read that as Vernon attempting to say something else (who knows what, honestly) and Harry hearing it as "Mimblewimble." It was Jo's simple writing genius and wit that turned this seeming jibberish into a spell. Perhaps this shows Harry's connection with the magical world: even without knowing it, he is hearing spells!

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My impression was that Vernon was saying some nonsense, and that it was written as mimblewimble just to show that what he said was nonsense, and doesn't mean anything at all.

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on pottermore "mimble wimble" is a tongue-tying curse, just putting it out there

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I never knew Mimble wimble was anything important. I also don't remember reading it anywhere else in the series.
I thought Vernon was so surprised about Hagrid showing up, he thought no one would be able to find them. I don't think he was just concerned about owls showing up, he might have realized that a person would show up to talk with Harry.
Wizards and magic were nonsense, so he just was sprouting nonsense.

Clarification: The spell Mimble Wimble is never seen anywhere in the books. It's just on Pottermore.

I think it's more likely that JK Rowling was sitting down to write spells for Pottermore and decided to put Mimble Wimble in there as kind of a funny nod to Vernon's nonsensical mumblings in the first book. It's a cool connection--almost like an inside joke for people who have an encyclopedic knowledge of the series--but I think it's a huge stretch to say that Vernon was trying to do magic. He's so vehemently against it that it just seems out of character.

I had always assumed that Uncle Vernon muttered something about Dumbledore and that Harry just heard wrong.

In context, Hagrid has just started yelling at the Dursley's for not telling Harry about the Wizarding World and it was Dumbledore's plan and Dumbledore's instruction for Harry to be brought up with the Dursley's away from all that. So Uncle Vernon might have started to try to say about how Dumbledore had told them so, in the letter that he left with Harry.

Doesn't the book say that Harry though it sounded like mimble whimble...
perhaps vernon doesn't actually say this but Harry has some instinctive recognition of spells and so interprets this as being what Vernon says

That's a really good point. I wonder if magic could be instictual like that.

I think mimblewimble is just a word people might say like "poppycock" or "codswallop." It might be one of those actual magic spell words that somehow filtered down over the years into the Muggle population without their knowing it's a real spell word. Maybe Muggles have been saying mimblewimble as an expression for centuries.