Remove the radiator, fill the holes & start over.
Those existing plugs are plasterboard plugs, but as you have brick behind, you can use regular 'rawlplugs' [generic 'brown plugs'] when re-fitting. You want to be properly fixing into the brick, not plasterboard &/or air gap.
Fill with something cement-based. Exterior Polyfilla or equivalent, which will be hard enough when cured to drill properly & be able to take regular plugs. If you can find something like that in a gun, it will make filling right to the back of the existing holes easier.
Don't put those toy screws back. If you're serious, then use at least 4" No8 or 6" No10 [100 - 150mm in new money] & no-one will ever pull them off. That will mean drilling 4-6" into the wall [borrow an SDS if you can get one, domestic hammer drills & brickwork are not great partners, you end up with conical holes rather than parallel sided], then sending two plugs in, one behind the other.