Is a 20,000 sample across 650 constituencies sufficient?

[MyNameIsArthur]

I was just watching Brexit : What The Nation Really Thinks on Channel 4 . A poll had been taken across the nation with a sample of 20,000 across all the constituencies. I did a quick calculation and that works out as an average of only 30 people per constituency. That doesn't seem like a very sufficient sample to me.

I keep getting stuff about TV programmes too, which I don't watch much of. The latest one was about advertising for bedroom furniture - again not something which particularly interests me.