When a controller is online under an approach or departure frequency, and when there is only one of those frequencies open, they need to control both roles. I was departing EGLL with no departure frequency available, when Heathrow Director Approach came online. I switched freq, checked in under IFR, and immediately was given a freq change. I was going to request a new altitude to not violate the SID I was under, and subsequently began multiple close calls with arriving aircraft on final.
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To clarify, Approach Controllers servicing departure aircraft is only recommended provided their workload permits and particularly if departures are likely to conflict with arrivals – which is indeed what you seem to be describing.
It’s best to DM the controller and give them feedback for improvement and/or for them to clarify the situation with you 
You may escalate this to an IFATC Supervisor if you so wish.
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