I want to categorize cities and counties in UK based on the region they belong to using JSON

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So I have two UK datasets, one has housing prices by cities and counties (housing_df), another has unemployment rates by region (unemp_p_df). I want to merge the two but the issue that I am facing is that none of the datasets have postcode or coordinates data in them. I tried using a GeoJSON file to put the cities in their respective regions.

I downloaded UK's (Counties and Unitary Authorities (May 2021) UK BFC) GeoJSON file from https://geoportal.statistics.gov.uk/ and have turned it into a dataframe with geopandas. picture of the resulting dataframe

How can I use this to categorize cities in one of my datasets into regions so that I can merge both of the datasets together?

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