Technically yes.
I've seen loads of "I'm a key worker, so back to school kids" posts on FB, of people taking the absolute fucking piss though. Half have a partner who is a SAHP or who, like my DH (in IT), is able to WFH. Its not going to be easy and we'll have to juggle our hours a bit and try to ensure the kids don't get too noisy while he's on a conference call but its doable, even in our tiny house.
I know a SAHM (who has a couple of rental properties) has filled out the key worker form wanting a place. Her husband, who always WFH anyway and frequently fields the kids, has an IT role for a company who possibly supports banking infrastructure.
. She might need school to babysit her kids while she "goes to sort out a tenant".
Practically anyone can squeeze themselves into keyworker catagory somehow. I work in a GP surgery and come into contact with patients all the time, as well as having to clean the isolation room. I'm pretty much guaranteed to get it at some point so don't want my children to spread it around my own local community. The clinical admin part of my role could be done from home if only the IT infrastructure were able to support it at the moment, but there are times when I'm on reception fielding patients, chaperoning or donning scrubs for the occasional HCA duties.
Don't get me started on the precious secondary parents who can't possibly leave their little darlings at home for a bit while they work, or are griping and moaning because there won't be a school bus to take them in.
If you have a partner who can possibly WFH, or non elderly, healthy relatives nearby, I'd seriously consider sorting something out. The letters state quite clearly that the arrangements are a last resort.
Good luck!