November 1st 1981 fell on a Sunday, so the weather man is correct, Bonfire Night (November 5th) is next week. However, the passage from the book states:
When Mr. and Mrs. Dursley woke up on the dull, grey Tuesday our story starts, there was nothing about the cloudy sky outside to suggest that strange and mysterious things would soon be happening all over the country.
Harry Potter and the Philosopher's Stone, Chapter 1 - The Boy Who Lived
So J.K. Rowling was actually wrong about the day of the week! It seems fictional weather reporters can be correct even if their creator isn't.
Funny how a statement as innocent as "The week starts on a Monday" can be controversial, isn't it?
Joking aside, a comment by Alex has sparked an interesting discussion in the comments about how the start of a week is different in different parts of the world. Here in Blighty, the convention is that the week begins on a Monday, after the weekend of Saturday and Sunday. However, I did like the comment from wizzwizz4 that the week, like a piece of string, has two ends, so starting and finishing on a weekend does make sense.
It is true that this wasn't always the case in the UK, and in fact I have struggled to find when the beginning on a Monday convention did become the norm. I've watched a few weather reports from the early 1980s which have been inconclusive, and looked at some vintage calendars on eBay which can start on either a Sunday or a Monday so also inconclusive. I'm leaving my answer as it stands though, as I do think most Brits would agree with my logic that the weather reporter is correct about Bonfire Night being "not until next week, folks!" if he is reporting on a Sunday.
Either way, I think we can all agree J.K. fluffed this one up.