Here's a USA-spec HRX model with the matching transmission; have a look:
It may just be a seal that's leaking (#15) so that is an easy fix. The trans should come out all the way, so you can properly top off the fluid level (since it has been leaking). ONLY USE Honda HST fluid; no other fluid is approved for use in this transmission. Honda's not trying to get rich off selling fluid, they just have their own spec and require it for all hydrostatic transmissions products.
I know the HRX537 is an European-spec model (made in USA) and Honda does have a distributor in Dublin: Here's a link to find a Honda Power Products dealer who can get you spares for this mower:
[url]http://www.hondaireland.ie/dealer-locator/[/URL]