I've got pretty much all the information on bronze age sword from the UK that is available. There's only two swords that have organic remains attached to them. One is from Ireland, and has remains of either antler or bone hilt plates, but they are in a very bad state. Another one has well preserved horn hilt plates (I'd have to look it up on my computer). There is also a sword with an organic pommel, but it's not described anywhere that I know. And lastly, a Mindelheim type sword was dredged from the Thames, which when found still had remains of a bone (?) hilt attached, but which fell apart and weren't preserved.
Aside from swords, there are some rapiers with organic hilts remaining. But I suspect you're looking for full-grip swords specifically?
As for wood, you can use any wood suitable for hilts that's indiginous. I personally prefer ash or yew (the latter is identified as an early bronze age dagger hilt).
The hilt shape on at least the Ewart Park swords is known from several bronze hilted finds. You can find reconstructions of these on my site: