I contacted the official Honda dealer in New Zealand. They confirmed that I need to replace the entire assembly, rather than just the arm alone. They are not the "pop out" variety. The cost is NZD305 EACH, rather expensive.
I contacted a local mechanic who said the same thing: need to replace whole assembly. He got a second hand one for NZD92, plus NZD28 labour. He assured me the second hand one is in good condition and should last a couple of years. I could have saved the labour cost the next time.
Note: Currently 1 NZD = 0.79 USD, or 0.49 UK pound
My car is the 2006 Honda Odyssey (Japanese version), model DBA-RB1. The strut assembly is made by Showa. I've included a few pictures of the old part that's been taken out: