In a theoretically perfect economic market you're right, but there is little if any evidence to suggest there is a causal link between economic displacement and wage growth. In fact wage growth at the low end has stagnated in London[0] despite the advancing economic displacement of it's low paid workers[1].

[0]: https://www.london.gov.uk/sites/default/files/Economy%20Comm... [1]: http://www.londonspovertyprofile.org.uk/indicators/topics/lo...