Yes. You can buy life insurance for anyone, as long as the identity of both the insured person and the person paying for it is confirmed and the relationship between you is stated.
Please note that the insured person will always be the “owner” of the insurance policy, and they are the only person who can choose beneficiaries and nominate instructions. So whilst you can buy life insurance for someone else, you cannot appoint yourself as the beneficiary of the life insurance – only the insured person can do this.