I'm Gen Z myself and this is worrying. I think the poll is a bit vague though. 'All or most cases ' - did that mean up to 9 months in all cases? Or up to 6 months with exceptions for severe conditions, as it has been for years?
I strongly doubt that the UK will end up restricting abortion more than most other European countries, becoming like one of the number of US states (Alabama for one) which ban abortion even in the case of rape seems very unlikely.
Could it be possible that in future the limit gets shifted to below 24 weeks, which is unusually high compared to most other European countries? Maybe. There are valid reasons to keep it at 24 though : some conditions may not show until then, some pregnancies may not be realised even.
I do think the push to legalise abortion up to birth was wrong and is backfiring. Most people in the UK want women to be able to choose up to the 24 week limit, I think, but I don't think most people support abortion beyond that, especially in the very late months when the foetus is closely developed into a baby and potentially viable- unless there is a very serious condition that risks the life and health of baby and/or mother. That doesn't mean most people want women to be aggressively investigated, I think it's more than in principle it should not be legally enshrined that abortion at 8 months or any time beyond 24 weeks is the same as what our law since 1967 allowed.
https://www.bbc.co.uk/news/articles/cx2dl5j0w23o