The Office for National Statistics website is going to be your friend here.
The current Population Estimates Dataset includes (under 'Mid-2016 detailed time series') national and regional population estimates going back to 1838.
For GDP there are several options, so it's probably best to look through the available data by searching the ONS website for '...
BEA: GDP by County, Metro, and Other Areas
The Bureau of Economic Analysis released the first official GDP estimates for the county level in December 2019:¹
"GDP by County, Metro, and Other Areas" on BEA.gov
Woods & Poole provide GDP for all U.S. counties. Unfortunately, they are a private, for-profit firm and consequently, the data has to be purchased. I would like to have had the database for all counties as well, but it was not necessary for my current research.
Their link is below. Finally, I would suggest reaching out to them and letting them know ...
It's only the US, but as a start, the Bureau of Economic Analysis (BEA).
Gross Domestic Product by Metropolitan Area
Real gross domestic product (GDP) increased in 292 metropolitan areas in 2015, led by growth in professional and business services; wholesale and retail trade; and finance, insurance, real estate, rental and leasing, according to ...