Do you really think that example is any wear remotely like this or any YOUGOV poll, If you do, I fear you don't have a grasp on reality, let alone statistics.
Go back to my real example about overtime. Ask one shift (A) who wants overtime and there is 50% take up, ask the other shift (B) and you get around 30-35% take up. That alone proves you need to ask everyone or a high proportion to get a realistic figure. YOUGOV has no control of who will be answering each of their polls, they can only base their poll outcome on the people who take the poll. As I said before their poll can only give an indication of what those who have done the poll want. Their assumption of what the rest of the country wants rest is a guess. Not even an educated guess because the difference in numbers is too big. Look at it another way, go back to my example, If you had only asked shift (B) how many wanted overtime and assumed shift (A) wanted the same, you'd fall short of what the actual take up would be. Take it one step further. with no prior knowledge of what each individual is likely to answer, randomly ask just 50% of each shift what overtime they want. There is a very extreme but slim chance that every person asked on both shifts will turn down the overtime, then just double the answers 2x0=0, so using your logic that YOUGOV are right, no one wants any overtime, yet there is 50% of shift (A) and 30-35% of shift (B) that does, but they won't get any because they weren't asked. Even if the 50% of each shift that was asked did include people that wanted overtime, there is no guarantee that you will still achieve the same take up, you could get 5%, 10%, on shift (A) you could even get 100% take up.
As I said before, if YOUGOV held the same poll again, just to keep things neat and simple, let's assume they get 1736 replies again. So long as it's not the same 1736 people answering again, it doesn't really matter if some do, whilst there is a chance you may get the same result of 60%, there is a chance of it being 80% or 40%, 100% or 0%. So you can't say that the results of 1736 entering a poll speak for the whole country.
I've copied and pasted direct from your YOUGOV link. The only additions of mine is underlining the two totally misleading statements