In respect of the MPL, on reaching 1500 hours you can (at your discretion) convert it to an ATPL by completing admin paperwork and of course providing the CAA with relevant payment. Due to the nature of the MPL the CAA would place a multi-crew restriction on it. This essentially means you can't therefore complete any single-pilot commercial ops or take a light aircraft out for a spin without first completing of the relevant training you'd otherwise complete within the PPL/CPL syllabus.
With that said though, graduates of Integrated ATPL programs are also unable to take single engine aircraft out without completing their SEP ratings.
If you fancy some light reading, you can find this in EASA PART-FCL Subpart F (FCL.405.A & FCL.505) in reference to upgrading to an ATPL. But to help you, I summarise the laws here:
When the applicant for of an ATPL(A) has previously held only an MPL, the privileges of the licence shall be restricted to multi-pilot operations but may be extended to single-pilot operations in aeroplanes, provided that the licence holder has completed the training necessary to act as PIC in single-pilot operations exercised solely by reference to instruments and passed the skill test of the IR(A) as a single-pilot prior to issue or any time thereafter.
Hope this helps you!