I'm saying they can't tell the difference between a neglectful family and an impoverished one or one with DC with additional needs.
Unwashed clothes- I've known families who can't afford the electricity costs to run the washing machine. If they have one, which some families don't. Also known families where they can't afford detergent so when they have a washing machine, they just run them through the machine hoping it'll get out most of the dirt. Which it doesn't completely and the clothes smell.
Also, many families who can afford to run the washing machine and detergent but don't have a tumble dryer or can't afford to use it so laundry hangs around for days in their homes in the winter not drying so it smells when worn.
Untreated headlice - a very few UK areas provide headline treatment on the NHS and only if you meet eligibility criteria. Most of the time, parents need to buy the treatments themselves which costs money out of an already stretched budget so may not be possible.
Nit combing with conditioner every few days will help, assuming the parent has the time to do that if working or doesn't have a disability that would make that difficult.
So it really isn't as simple as teachers 'knowing which kids are being neglected' based on your examples and if those teachers suspect that to be the case, they should be referring to CYPSS as it's a safeguarding concern which teachers should be well aware of and commonly, have safeguarding lead practitioners in the school.
If teachers are not making those referrals, that's a shit school not meeting it's statutory obligations and if you worked there, you are responsible to flag concerns to the designated safeguarding leads.