https://www.tomforth.co.uk/circlepopulations/
Have a play around with this. Within a 10km radius of the centre of Cardiff, there’s 442k people.
Coventry - 500k
Southampton - 529k
Leicester - 597k
Nottingham - 663k
Newcastle - 691k
Bradford - 715k
If you want to be properly nerdy place the centre point on each club’s stadium. I can’t be arsed however.
Regardless of what arbitrary boundaries on a map say, Cardiff is not a “big city”. It’s medium sized and growing.