When he was housing minister, he did indeed claim that “migration pushed up house prices” – a claim which was later dismissed:
https://www.bbc.com/news/uk-politics-43753564

One wonders, then, to what extent the migration of his father from Czechoslovakia “pushed up house prices”…

It was between 1938 and 1939 when “the British Schindler” evacuated hundreds of Jewish children from Prague:
https://www.express.co.uk/news/uk/588091/Nicholas-Winton-saved-children-Nazis-dies-106

And as part of this “Kindertransport”, it was one of these children who was the father of the former Brexit minister:
https://www.timesofisrael.com/dominic-raab-karate-kid-with-a-jewish-father-in-the-brexit-hotseat/
https://www.thejc.com/news/uk-news/brexit-secretary-dominic-raab-jewish-refugee-1.466795

The “frontrunner to be PM” is in fact very proud of his roots and his “determination to fight racism”:
https://jewishnews.timesofisrael.com/brexit-son-of-czech-jew-dominic-raab-frontrunner-to-be-pm-if-may-ousted/

But, then Raab is not the first politician of foreign extraction who would limit foreigners’ entry:
https://www.history.com/news/donald-trump-father-mother-ancestry
https://www.independent.co.uk/news/world-0/donald-trump-immigration-rule-germany-grandfather-visa-english-language-skills-stephen-miller-jim-a7876121.html

“It’s those whose families have arrived … within the last generation or two who are often the keenest to slam the door shut on those coming today.”
View at Medium.com

What is even stranger still is that Dominic Raab’s wife is also not British-born:
https://www.getsurrey.co.uk/news/surrey-news/surrey-mp-who-czech-refugee-11424826