You don't necessarily have to pay the new minimum wage rate from 1 April, which is when the new rates are effective from. You need to start paying the higher rate from the start of your first pay reference period after 1 April. So if you run your pay month from 15th of each month, you don't have to pay the increased rate until 15 April.
Further information
Letter advising of pay increase due to increase of the NMW/NLW