Labour in the UK didn't win by a slim margin. They were +10% of the popular vote and have a landslide majority in Parliament. It hasn't been unusual in the past for a govt in the UK to win while losing the popular vote, so they do have a mandate.
You may be technically correct but the comment above has a point. It’s not a strong mandate, and it’s more fair to emphasize that the Tories collapsed than that Labour won.