Jelly, on an ATC clearance in CAS a pilot doesn’t have to comply with the 1,000ft rule, as in the case here, but there is no exemption from the 500ft rule*. Complying with the latter is forever more difficult over London due to the increase in high rise building projects; technically speaking consideration must be given to separation, even when following the published heli-routes!
Twin engined helis (obviously not singles) are commonly given direct clearances such as the one you heard.
*I do know of one pilot of a twin engined heli who bust the 500’ rule in a very blatant way trying to continue on the commonly given BRENT - BATTERSEA clearance in very low cloud and was reported to the CAA.