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diver
hedge school masters
inured
both correct

So hard this week, never heard of hedge school master.
Is 31a Off one’s trolley:
I walk on ice, turning you mad (3,4,7).

41 correct
one - I
off - ice( (kill)
stroll
ye - you (reversed)

31*

Thank you.
43a admired one’s having nothing to do with dictator (4).
I?o?
Maybe idol?

48a Re-engage, presumably, after finally playing volley (7)
G?n?i?e

53a Mate to duck out of duty initially, and degenerate (5)
D?a?e

43 Yes, Idol, admired one. The dictator indicates 'sounds like';, sounds like idle, having nothing to do.

53. Drake, male duck. D, duty initially and Rake, degenerate (noun).

In response to various comments, didn’t bother with writing the clues as I assumed anyone replying would have the puzzle in front of them. Anyway, many thanks for the help - all completed now. On to the Listener.

43 homophone (dictator) of idle (nothing to do)
48 UN-FIRE (re-engage) after G
53 D + RAKE

Thanks again, it’s quite demoralising when you’ve got all the crossing letters and still can see the answer.

Still a long way to go with this.

38a Made over five hundred European visits without protesting (10)
Begins with 'r'.

45a Willing female volunteers in experiment, one run by hosts (9)
Begins with 't'.

29d Group that has lately been rolling off our neighbour's tongue? (8,6)