I worked for... a major, household name multimedia organisation. The bosses forced everyone back into the office, five days a week, even people who worked anti-social shifts, within days of lockdown ending. They were really heartless about it. The result? Most of the women left. I think Labour is looking at formalising wfh requests - I don't know the details. I know there are bad stories on Mumsnet about parents taking the Mickey with wfh, but I don't think that's the norm - certainly not in my experience.
wfh is a really important feature of a work-life balance for many people, including families, and a lot of people work faster and more efficiently when not at the office. If somebody is the kind of person who will clown around and not bother with your job, they're going to be doing that regardless of whether you're at home or in an office and management need to monitor that - not penalise everyone who wants to wfh.
I think your concerns are valid, it's worth looking at what Labour are proposing and perhaps talking it through with your line manager. It's a funny time for your company to be implementing this if the government is seeking to bring in changes. Ultimately, you'll manage no matter what, because that's what all parents have to do - whether it's paying for childcare etc. But I don't see that people with young children, particularly women who statistically face far more caring demands, should have to. The solution is out there - but companies need to get to grips with it. Given that most of them are run by men, however, the shift is going to take some time.
Meanwhile, good luck - hope it works out for you.