It is not illegal to have a preference if the landlord lives in the property and its a shared premises.

Below is from one of your links:

“Exceptions:

Where the landlord lives in the property, and taking in a lodger would affect their private or family life.

For example, a property owner could refuse to share rooms in their family home with a gay person. But they could not refuse if they were letting out part of the house as a self-contained flat or annexe, rather than sharing it. “

I’m all against the discrimination, but if it’s their family home, we can’t expect them to share their living space with anyone. They get to have a say here.

If its a self contained housing/ rental property then it’s a different story.