A good rule of thumb is that upper-class people in England will pronounce everything, but they usually won't put more space in between the words than they physically must.
So "I've won" would be "ivewon" (I don't know the phonetic alphabet, but the Slovak transcription would be close to "ajvuon", with a slight stress on the "uon". The v sound will transform smoothly into the w sound by rounding the lips and pushing them forward a bit.
And "months" would be "muhnΘs" with the "uh" a slightly o-sounding schwa and the final s an s not a z. I can't do a Slovak transcription because you don't have that short u or the theta.
The working-class pronunciation might not be much different, except that the person might be more likely to say "I won" rather than "I've won".
If you listen to the BBC news broadcasts, you'll hear an educated accent that's very acceptable socially.
English pronunciation is a big problem because English is technically what's known as a creole language. That's defined as a complete, fully-functional language that was created by gluing together big parts of other languages.
The languages that formed English are Old Low Saxon (also called Anglo-Saxon), which was a mix of dialects from southern Sweden and the islands off the western coast of Denmark, plus the dialect of French that was spoken on the north coast of France around the year 1000 CE. It was called "Norman French" because it was the dialect of Normandy, which got its name from being invaded and conquered by the Normannen, the Vikings.
The Saxon formed the substrate spoken by the working people of England, and the Norman French formed the superstrate used by the elites who gradually conquered all of England starting with the southern coast in 1066 CE.
In his novel Ivanhoe, the Scots author Sir Walter Scott pointed out that the thousand-year-old (800 years old in Scott's time) social divisions are still reflected in our modern English language.
The example he gave was that when non-humans are referred to while they are alive, we use the Saxon terms, but once they've been slaughtered and their corpses cut up and cooked for the table, we use the French terms. So "cow" (Saxon cu) becomes "beef" (French boeuf), "swine" (Saxon svin) becomes "pork" (French porc), "sheep" (shaap) becomes "mutton" (mouton) and so forth.
Since the Norman French really didn't care about the Saxon substrate, the spelling of many originally-Saxon words in English still reflects some long-dead scribe's idea about how to represent the pronunciation of some local Saxon/Anglish/Frisian dialect that nowadays hasn't been heard in a thousand years. Languages like Slovak don't have that problem -- they developed in a natural way.
Add all the words that have immigrated (or in some cases were forcibly grabbed and dragged in) from other languages, and it's really a wonder that any anglophone can spell any word right three times out of five. There've been attempts to establish more sensible conventions, but like the Gaels anglophones seem to take perverse pride in how hard it is not to make spelling mistakes.
But our current spelling conventions are not very old anyway -- it's only been since the 19th century that there's been a way to make paper out of wood chips rather than rags, as was the practice til then (those books in the library that are 300 years old yet the paper still looks fresh and new? That paper was made from rags, usually linen or hemp. The rags didn't cost much, but rag paper was/is expensive to make, because it had to be made sheet by sheet, by hand).
It was the invention of wood-chip digesters and cookers, and the Fourdrinier paper-making machine that finally allowed books to be sold cheaply enough that anyone who wanted one could buy a dictionary and look up words to see what the current spelling convention is.
Here's a small example of why pronunciation is so hard:
The word "two" (the name of the numeral 2) is pronounced "tu" today, but how would anyone ever know that? It seems crazy.
But the corresponding Scots word is "twa" and is pronounced "t'wa". aha!
If you read Chaucer's Canterbury Tales in Middle English, you see that "two" was originally pronounced the way it's spelled: "t'wo". There's no way to figure out today that "two" should be pronounced "tu", but in Chaucer's time (late 1300s) the spelling was a guide to the pronunciation.
But we kept the spelling and changed the pronunciation! Instant craziness.