If it's one chase in Breeze block and you don't want to buy expensive SDS drills and bits then can't beat a club hammer and bolster. It is quite an art form controlling a sds drill especially in breeze block or soft brick. The old way is less messy and you will be able to control that mess a lot better
If it's hard brick then you might want to think about investing in a SDS drill. Wicks a few moths ago were doing their own range for about 40 pounds and for diy use pretty good value. In fact the bits were dearer than the drill.
Would pay as well to just gen up on the building regs to make sure you don't go to deep and what zones to run the cables in
Depends what your walls are made of, if your chasing out a wall that has been base coated and plastered, you will just need to chisel out the plaster work and the cable should be able to be clipped to the brick/block work without the need to chase in to that, leaving enough gap between wall finish and cable to repair the plaster work.
Remember the cable should be routed in the permitted safe zones.
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