As I bimble around the UK in either a non-radio or single VHF radio fitted aircraft, I am blissfully unaware of the presence of TDAs and SAR Operations. Unless the ATC unit I am in contact with decides that the TDA is within its patch and decides to rebro the information. Outside of that big sky/little aircraft theory prevails.
A TDA protects a SAR aircraft from military flight only as the SAR crewmay be degraded in lookout (all eyes searching) or unable to manouvre (200 feet of rope out with a hero swinging underneath)
According to the DAS publication, As a non-military pilot I am not required to avoid a TDA unless the person with responsibility for the administration of that TDA specifically requests me to leave where upon it becomes a legal requirement.
If the SAR Operation requires complete sterilisation of airspace then the emergency co-ordinating authority should instigate a TRA.