Simple answer: Yes.
As long as you're in England, Wales or Northern Ireland (because the law is different in Scotland) anyone is free to leave their estate to whomever they like (irrespective of whether they're family members or not) and, equally, to exclude whomever they (dis)like from their will. They never need to notify people about whether they're included or excluded from a will.
However any child of a deceased parent (among others) has the right to apply to a court to vary the terms of the parent's will on the grounds that the will failed to make 'reasonable provision' for them. [NB: A court will NOT automatically approve such an application. The applicant needs to show that there's a valid reason for them to receive something more from the estate than they've been left under the terms of the will]