This had broken due to the weight of the items in the drawers causing the brown plastic runners to break. It's not that easy to find replacement runners, and in any case, they are likely to break again if they are used with this much weight - the unit is clearly designed for clothes, not paper files. It was clear that I needed to find a metal runner that could fit in the same slots to replace the plastic runners.
Luckily, the slots in the drawers are a standard width and length: 17mm width and 350mm length, so these metal runners fit.
They need securely fixing into the chipboard side panels, but an ordinary wood screw is not going to be able to take the weight. The pressure on the bits of chipboard just under the screws would be too much and the runners would fall off. On a similar IKEA drawer unit, the runners are fixed with M6.3 euro screws which have a distinctively wide thread and short fat design. But these runners have 5mm clearance holes which cannot take an M6.3 screw, so I found these M5 euro screws which work very well into a 4mm hole, drilled blind to a depth of 10mm (in otherwords, you don't drill right through the side). Using a bit of tape on the drill bit allows you to see when you have drilled in far enough.
Pencil markings on black foiled chipboard just aren't visible enough, so I dug out an old correction pen which draws a bright white line.
It is important that all the runners are mounted the same distance from the front edge so that the drawer fronts will be aligned. Getting the runners in the right location vertically is less of a problem because I used the holes from the old runners for alignment - their centers are the centers for the holes for the new runners. However, you do have to get this exactly right or the drawers will hit each other when you close them.
Finally the drawers are fixed to the sliding part of the runners using M4 x 12mm pan head machine screws, which I bought from RS Components. These fit through 4mm holes drilled in the sides of the drawers using one runner as a template to mark the hole locations, and into the threaded holes in the runners. You need to use exactly the right length screws for this, otherwise you will prevent the drawers closing.
Total cost of repair £18.71