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When I sat my ATPLs (under CAA) a buddy of mine was finishing off the last few exams just before he completed his IR. So you can start you flying.
However, if you fax the CAA with you request I'm sure they will fit you in. Well they did a few years ago when I forgot to book my exams until a week before the exam date!
Give me a call tomorrow if you want a chat about it.