The new ATSOCAS state that it is the pilot's responsibility to request the type of service required. If this isn't stated in the first call then you can probably expect the controller is offering the level of service he/she is prepared to give, taking into account their current and expected workload.
There is no SOP, controllers are expected to provide the full range of services as appropriate so will upgrade where possible on request - however traffic inside controlled airspace always has priority over that outside. If the controller feels they cannot take on the responsibilities of a DS then they will offer a TS or BS - and yes, there's a big difference in the workload! DS cannot be provided below 5000ft, so if you are calling MAN on departure this could be why you are initially offered a TS.
Your comment about IFR not wanting to manage its own separation sounds a bit worrying to me though - regardless of the type of service agreed on, outside controlled airspace collision avoidance remains the responsibility of the pilot, and you cannot assume that a DS will be available. Outside CAS we have no idea of who/what is operating and what it is doing, and whilst we will try and give traffic info/avoiding action its not always easy when unknown aircraft pop up suddenly or change direction. I would hope that the pilot is keeping a good look out - after all, radar has a time delay!
There is no 'standard' offer of service level. Its just what fits at the time. DS has quite a level of responsibility for the controller in an unknown envronment. Why offer it if the pilot only wanted a BS in the first place?