I have grown a few hundred Echeverias here including as indoor plants so I have some experience with the genus.
The pot size is fine for now. Make sure to empty the saucer after you water. True, the soil should be faster draining, like regular potting soil (or compost if that's what you call it across the pond, the product for potted plants) with an equal amount of perlite, pumice, or lava rock mixed in. If you can remove the plant without disturbing any roots, like it just pops out and the extra soil falls away, great. But you really don't want to be messing with the roots while the plant is in crisis. Definitely keep root manipulation to a minimum.
Whatever you do, be very careful not to water right after repotting or handling the roots in any way... wait a week to water.
