Here's an example of it being used as a slur

Here's an Irish politician talking about her child being abused as a "mongrel" to prove it's not just a UK thing

Here's a link to a Nazi children's book titled "the mongrel"

If you refer to a human as a mongrel, you are definitely making a pejorative comment about that person's origins.

(often derogatory) Someone or something of mixed kind or uncertain origin

Since you're a fan of quoting Wikipedia - In December 1939, Himmler declared that racial assessments were essential to avoid "mongrel types from emerging in the territories that are to be newly settled. I want to create a blond province."

Precedent in UK law for hatecrime charges for calling someone a mongrel will be harder to track down.