Expanding on that if you are following a SID/STAR and are given a "direct to" does that mean that you are(flightcrew) soley responsible for terrain sep.
No. In the UK...
13.1 Controllers are to ensure that levels assigned to:
a) IFR flights in receipt of a radar control service
b) flights in receipt of a radar advisory service and
c) flights in receipt of a radar information service and receiving vectors;
provide adequate terrain clearance...
Unless the "direct to" takes you outside controlled airspace, the level assigned in the ATC clearance must ensure terrain clearance.