I am now at the stage on my layout where I want to start wiring it up a bit. However, I need to drill through polystyrene then plywood to create channels for some of the wires.
And in some instances it will be 150mm+ deep.

What would be the best type of drill bit to use?

A drill bit going through polystyrene would be a disaster in the making.  Make a hole in the polystyrene with a hot wand styrofoam cutter (about £15 on Amazon) and then drill the hole in the wood after. Make sure the hole in the polystyrene is bigger than your drill bit and try not to let the drill hit the side of the hole on the way through. 

Expanded or extruded polystyrene?    To be honest either way I'd poke through the polystyrene with a bradawl or similar sharp pointed stick thing eg. kebab skewer No need to drill it.   Drill the ply first from underneath then insert the poking stick  

I hate to say it but if you've ended up with thick polystyrene on top of ply that would surely have been a prime candidate for an open-frame baseboard?

Quote from: ntpntpntp on February 12, 2024, 02:25:44 PMExpanded or extruded polystyrene?    To be honest either way I'd poke through the polystyrene with a bradawl or similar sharp pointed stick thing eg. kebab skewer No need to drill it.   Drill the ply from underneath.

I hate to say it but if you've ended up with thick polystyrene on top of ply that would surely have been a prime candidate for an open-frame baseboard?

I live and learn