Employer not paying me until a month after SMP

[ttcchapter1]

But if context, been working with the company since January 2019. Went on Mat Leave in December 2020 with baby due in Jan 2021.

Got an offer for a very good WFH job in April and handed my notice in. They accepted the notice with effect from May and terminated the employment in May but said they would pay me my holiday pay after my SMP ended in August. (Not sure why they did this)

Now come August they have decided they're only paying me my one weeks SMP for this month and will pay me my holiday and notice pay at the end of September!! Not only is this inconvenient but really messes up my budget. Why delay payment a whole month later?

Contacted ACAS and have gone back to them as ACAS have said it is illegal to withhold this payment from me considering employment ended in May.

AIBU to take further action if they don't pay me in August instead of the end of Sep?

I don't know much about this area at all but I just gave this a quick read - maternityaction.org.uk/advice/resigning-from-your-job-during-pregnancy-and-maternity-leave/

Looks like you get paid the full 39 weeks regardless of handing in your notice (so long as you haven't started your new job) and it seems understandable they'd probably pay your left over holiday as a lump sum in the pay packet following the final SMP payment?

Would that fit with the timelines they're suggesting?

That page does also mention that employers can choose to pay SMP and leftover holiday as a lump sum before the end of the 39 weeks so you could ask about that instead maybe?