OK, following your hints didn’t take me exactly to the solution but caused me to realise I had missed a chunk of the storyline by getting to the Oxford Dig too soon. I managed to trigger the start of the Oxford sequence (protect the golem) and this jumped me to tier 11 - collect three statues and kill khenti. I still can’t get into the Lost City but the quest has clicked over into tier 12 (speak to Nassir) which I believe will set me on the Last Train to Cairo sequence. Hopefully along the line I will pick up whatever I need to open the gate.
Thanks again.