A bit of an update:
I finally managed to get some work through a new agency and used the opportunity to do my tacho print outs for the days I worked for the non-paying agency. Good thing I used to do manual entries at the time to mark the actual shift start time.
I’ve sent them a (tracked) “letter before court claim” giving them 14 days to respond.
ACAS turned out to be pretty much useless for my case because I have no contract of employment and the payslip doesn’t have the correct amount of hours and rate of pay, it’s not even from the company I’m claiming from. I tried calling ACAS 3 times after submitting an “Early conciliation request”, each time I was on hold for 5 to 10 minutes. They did call me once - last Friday, to let me know that my case was about to expire but I wasn’t home at the time so was unable to provide them with details, tried calling again later that same day with no luck, today I decided to go on on my own with the small claims court if I don’t get my money in 2 weeks (+time for the letter to be delivered)