dunno - it isn't quite so simple as I first thought, but it should be possible with a bit of perseverance. In addition to the fan which you need to check (as per jbartos): because the brush positions can be shifted as you describe, this may mean that they are not set to the neutral position but are shifted say 10 or 20 degrees in the direction against rotation – for a motor. This is done to reduce sparking at the brushes due to an effect called armature reaction, where the magnetic field in the motor is distorted due to load current in the armature. If you reverse the direction of the machine, the brush positions will have to be shifted by the same amount the other side of the neutral.
The neutral position for the brushes coincides with the axial centre line of the main poles i.e. the stationary windings mounted on laminated poles around the bore of the motor housing. As you have 4 brush positions, you should have a 4 pole motor i.e. there are 4 main poles.
Incidentally larger DC motors (supplied with DC), particularly those meant to be reversible, usually have the brushes in the neutral position and instead have additional windings (interpoles) placed between the main poles, and possibly even compensating windings mounted in the pole face of the main poles, to reduce the sparking. I doubt very much that your universal motor will have either interpoles or compensating windings. Relying on the brush position shifting has two disadvantages:
1. the ideal position for the brushes depends on motor current - higher loads ideally require a larger shift, so some compromise may be required if the load is variable.
2. if the motor is reversed, or changes from motoring to generating, the brush position must be shifted to the opposite side of the neutral position.
Hence the technique is only used on relatively small motors. You may have to experiment with brush position to minimize sparking at the brushes.
To achieve reversal then, you should find that every other brush holder is connected together. If you shift the connections around by 90 degrees (ensuring that opposite brush holders are still connected to the same point), and if necessary move the brush positions to minimize sparking as previously described, you should be in business. You may want to experiment with on reduced voltage at first, ac or dc.
I hope this all makes sense. Metropolitan Vickers was an old UK company by the way, they disappeared nearly 40 years ago so you do have an old machine!