The statutory entitlement of one or two consecutive weeks’ leave (known as ordinary paternity leave) must be taken between the date on which the child is born or placed with the adopter and 56 days after that date. However, if the child is born before the first day of the expected week of its birth, the timeframe for taking paternity leave ends eight weeks (56 days) after the first day of the expected week of its birth

Therefore, if the employee falls sick just before they were due to take their paternity leave and wishes to delay it, they would need to ensure that they exercise their right before the end of the 56 day period (from the date of birth or adoption).