Penalties from HMRC will be issued if any late filing of a Full Payment Submission (FPS) from 6th April 2016 onwards.
Currently there is a 3 day relaxation for filing a late Full Payment Submission which is detailed per the HMRC website GOV.UK https://www.gov.uk/guidance/what-happens-if-you-dont-report-payroll-information-on-time
"HMRC won’t charge a penalty if:
• your FPS is late but all reported payments on the FPS are within 3 days of your employees’ payday (this applies from 6 March 2015 to 5 April 2016)"
The other circumstances where HMRC will not issue a penalty for late submission of an FPS are when:
• you’re a new employer and you sent your first FPS within 30 days of paying an employee
• it’s your first failure in the tax year to send a report on time (this doesn’t apply to employers who register with HMRC as an annual scheme or have fewer than 50 employees for the tax year 2014 to 2015)