The consultation summary that was produced in February is also still available should you wish to see it: https://www.gov.uk/government/consultations/appropriate-measures-for-permitted-facilities-that-take-healthcare-waste
Instructions from the EA are that operators will be required to meet the new standards at new (or substantially changed) sites but for existing sites EPs will continue to reference S5.07 until they are varied through the permit review process.
The next step in the permit review process is for the EA to formally issue sites in the healthcare waste sector with a Regulation 61 Notice, which will need to be completed and returned within a set timeframe.  This will set out your current measures and what will be needed to comply with the revised guidance.