AOG
That's exactly right. The proprietors can say, "Sorry, we're full", without giving an explanation as to why they are not offering a room.
This is key to the issue.
The mistake that people are making is saying, "We are not serving you because of your race, ethnicity, sexual orientation, or because of a disability."
As a business-owner, you can discriminate to your hearts content - there's no law which states you cannot refuse service to someone who is abusive, drunk, violent or 'inappropriate' (eg. a child who wants to enter a betting shop). But the Equality Act 2010 forbids businesses from discriminating based on the concepts as outlined in previous acts, to whit:
Equal Pay Act 1970
Sex Discrimination Act 1975
Race Relations Act 1976
Disability Discrimination Act 1995
Employment Equality (Religion or Belief) Regulations 2003, Employment Equality (Sexual Orientation) Regulations 2003 Employment Equality (Age) Regulations 2006