I assume that they are referring to AMC1 to Appendix 3, A.(a) - "The ATP integrated course should last between 12 and 36 months. This period may be extended where additional flying training or ground instruction is provided by the ATO." Although this is only an AMC, the convention under EU law is that published AMCs are mandatory unless an alternative means of compliance has been accepted by a member state. In this case there is no alternative means of compliance and so the de facto limit for an integrated ATPL course is 36 months from start date of the course. It is possible that the period may be extended but that will be solely at the discretion of the competent authority. There is nothing that CAE can do about it, you must speak to L&TS Policy at Gatwick.
The skill tests and examinations that you have passed will remain valid for the periods stated in Part-FCL but because the integrated training course is not valid, you would have to meet the individual experience requirements for issue of the CPL (200 hours total time, including 100 hours PIC, etc.), MEP (70 hrs PIC) and so on.