This spelling, which is considered an error, occurs in both American and British English, and probably, as Dan Bron's comment says, everywhere.

The reason for the spelling is that of and have have the same pronunciation in this context: /əv/ or /ə/.

This pronunciation is what English language teachers call a "weak form", meaning it is a pronunciation that occurs only when the word is unstressed. Many common grammatical words in English have weak forms with the vowel /ə/, and strong forms with a different vowel. Another example is to, with the weak form /tə/ and the strong form /tu/ (rhyming with do, and homophonic to two and too). The strong form of "have" is /hæv/, with the same vowel sound as "hat" or "cat". The strong form of "of" is /ɒv/ in British English; in American English, the strong form of "of" is usually /ʌv/.

Michael Harvey's comments saying that "of" rhymes with the first syllable of "hover" are referring to the strong form. However, I doubt that anyone habitually uses the strong form of of in this context. I would only expect to hear "of" in a strong form here in the artificial context of somebody who is reading out loud and making an effort to make "would of" sound distinct from "would have".

Spellings like "would of", which are considered erroneous, occur in both American and British English, and probably, as Dan Bron's comment says, everywhere.

The reason for the spelling is that of and have have the same pronunciation in this context: /əv/ or /ə/.

This pronunciation is what English language teachers call a "weak form", meaning it is a pronunciation that occurs only when the word is unstressed. Many common grammatical words in English have weak forms with the vowel /ə/, and strong forms with a different vowel. Another example is to, with the weak form /tə/ and the strong form /tu/ (rhyming with do, and homophonic to two and too). The strong form of "have" is /hæv/, with the same vowel sound as "hat" or "cat". The strong form of "of" is /ɒv/ in British English; in American English, the strong form of "of" is usually /ʌv/.

Michael Harvey's comments saying that "of" rhymes with the first syllable of "hover" are referring to the strong form. However, I doubt that anyone habitually uses the strong form of of in this context. I would only expect to hear "of" in a strong form here in the artificial context of somebody who is reading out loud and making an effort to make "would of" sound distinct from "would have".