Sounds about right, although I don't really understand the 'in parallel with...' bit - don't you need the CPL (or ATPL) exams complete before the CPL skills test?
An possible alternative would be to get the Class 1, start the ATPL writtens and then at a suitable point (after module one?) go do an FAA Multi/IR. Then go back, get the ATPL writtens done, do the CPL flying and then finally fly the 15 hours needed to convert the FAA IR to a JAR IR. I'd bet that having an IR would make the CPL test easier, and it's prbably a cheaper route to an JAR IR (the FAA will credit you with some of the IMC training hours, so it's around 25 hours in the states plus 15 here, rather than the full 55 here - IIRC, of course
).