Hi,
I had to do the same thing with an FAA licence.
You can only convert the flying portion when you pass the 14 exams (for a full CPL/IR), you can start it but it would be foolish as your currency and rustiness will set in. Put aside 4 months absolute minimum to do the 14, then a further 4 weeks to convert (perfect VFR and no backlogs with examiners).
The minimums you can do are as follows:
For the CPL Conversion - Hours as required
For the IR Conversion - 10 hours sim & 5 hours aircraft
Also factor in the following:
Test fees:
CAA - £691 x2, £60 x14, £210 licence issue, Class 1 Medical £450ish
At the school:
RT exam - £35, £100 x2 170A Test Fee
Weather in the UK being **** - extra 4 - 6 weeks accommodation