Qualifying for free school meals DOES mean that a child is flagged within the school (which may be what badbudgeter meant), but NOT that they are referred to social services. The school actually receives additional funding for each such child, called pupil premium. That's why you should apply even if your child is KS1 and getting free meals anyway - why turn away £1455 for your child's school?! Yes, there will be a marker on your child's school record if they qualify for pupil premium, but it should be confidential.
Statistically, children in this category do not do as well at school; that's definitely not the case for each individual child, but it's a rough-and-ready way of diverting funds to schools that might need a bit more. There will be some "pupil premium" kids who are doing just fine with no intervention, and there will be some kids who don't qualify for the label who do need some support. Teachers are well aware of that. Hopefully those groups balance each other out reasonably well so that schools get roughly the "right" amount of extra funding.
Schools are measured (amongst many things) on whether pupil premium kids (on average) are falling behind the others - that's not any reflection on individual kids, but just to try and check whether the school is doing enough to support all children in making progress.
The pupil premium label can sometimes mean things like free places on trips, vouchers for food in holidays, access to holiday activities, etc, so there's sometimes a direct benefit for the individual child.