Is it legal for a room advert to say only one nationality or race can apply?Beta*

Usually not. Refusing someone because of their race, nationality or ethnic origin is discrimination under the Equality Act 2010, and that includes adverts that say only people of one nationality need apply. There is a narrow exception: where the landlord or a near relative lives in the home and shares living space such as the kitchen with you, and the home is small, the rules on choosing who to let to don't apply in the same way. A letting agent or a landlord who doesn't live there can't rely on that. You can report a discriminatory advert to the website it's on, and get advice from the Equality Advisory and Support Service.

Sources: Citizens Advice: discrimination in housingEquality Advisory and Support Service