[spiracles]

Can anyone advise?

Over the past week my courgette plants indoors have started to develop white spots and leaf damage.

What is wrong, and are the plants doomed?

[Sneachta]

They look pretty sad alright, they certainly look sick and floppy. Possibly fungal infection?, I'd be inclined to try putting them outside during the daytime and get a bit of sun and fresh air on them to see if they perked up.
Not too late to start some fresh ones (in different compost might be a good idea too).

[Greengage]

i see they are only producing their first true leaves, looks like water damage maybe scorched by sunshine, water well and feed, Its very hard to kill plants they will want to survive so dont give up yet.