IIRC the limit according to the standard is £100,000/day but most banks impose their own arbitrary limit. Assuming things haven't changed in 5 years, this[1] lists the limits for a lot of banks. I can also add to the list that Monzo's is £10,000/day.
BACS is generally cheaper at volume. In addition, BACS Bureau allows a payroll company to transfer money directly from your employer's account to yours without the money ever reaching their account.
All fixable, but payroll companies are generally chosen on price, not innovation.