If it was going in my house and assuming that the mantle is >50mm thick then I'd do as follows:
1. Drill four 10mm diameter blind holes, 25mm deep, in the underside of the mantle, two per brick support along the plane perpendicular to that of the mantle.
2. Resin fix 8mm diameter threaded steel rods (stainless if mantle is oak) into the holes in the underside of the mantle. Rod length to be at least 75mm.
3. Place mantle on brick supports and mark exact locations of rods. Drill 10mm diameter holes in supports to suit actual rod lengths.
4. Resin fix rods in brick supports using temporary wedges/packers to keep the mantle level.
Now, if your mantle isn't oak then you could use a "machine thread to wood thread" screw instead of threaded rod eg screwfix part number 11850-12 but that may also depend on the thickness of your mantle. I always keep some threaded rod in stock including resin since you can make all manner of repairs with minimum fuss.
HTH,
C