The street name suggests a derivation from the area of Tir-y-berth near Hengoed in the Rhymney Valley.
There's a Tir-y-berth Street in Gelligaer, which is nearby, but the appearance of the houses on Google Streetview suggests post-war construction - though they might possibly be immediately pre-war.
Letters to local newspapers circulating in the Rhymney Valley summarising your known facts might get a useful response.
Can't advise on evacuation records, I'm afraid - no experience of that area of research. This TNA webpage may help you a little: http://www.nationalarchives.gov.uk/records/looking-for-perso...