At the moment it is illegal under EU law for MBM to be exported from the EU to 3rd countries for incineration.
The EU is considering amending their Regulations to allow the export of MBM outside the EU for combustion but this has not been approved yet.
If approved then the UK sites currently incinerating EU derived MBM would need to be approved / permitted under the ABP Regs and Environmental Permitting Regs for combustion of MBM.
The UK has not yet confirmed its position on whether MBM is a waste or can be considered as a fuel. See also the Border Protocol Delivery Group Border Operating Model