I would not be surprised if the answer from CHIRP is "don't check in on a new frequency until you are ready to accept an instruction". There really is no rush to check in with the radar controller in the UK. I often wonder what pilots are trying to achieve by telling the tower controller they are airborne, ie attempting to prompt a frequency change as the wheels come up.
SIDs in the UK are all designed to provide separation from other traffic. If you just fly the SID and check in once you've finished cleaning up everything will be fine. It doesn't matter if you are sitting on the frequency for a bit without having said anything - separation is assured.
G W-H