Is it not possible to complete conversion training for all at bartolini and then apply to CAA for the issue of my UK based license?
Yes it is possible.
However under ARA.FCL.205 examiners are required to be monitored and the UK CAA exercised their responsibility to do so.
Rumour has it though, that the CAA were not impressed with the standard of examining and as such the examiners in that area are no longer authorised to conduct testing on behalf of the UK CAA, and when you apply for designation of a CPL or IR skills test they will allocate a UK examiner not one of the Polish ones, so the school make you switch your medical to Poland or elsewhere.