Unless I miss understood him Shadespyre was talking about hanging someone from a tree, not using the wood for a gallows...
Yes, that's correct. From my reading so far it seems that the famous place of execution at Tyburn, London was referred to as "the elms" even in Norman and later times when a gibbet existed. I haven't cross-referenced yet, but I assume this is due to an Anglo Saxon and/or Norse tradition.
I saw an excellent show by comedian Wil Hodgson about British Hangmen in Edinburgh this summer (it wasn't a comedy show per se, but contained humour nonetheless). Similarly I can see how a comment I intended to be darkly and ironically humorous good be considered in poor taste with insufficient context, so sorry for that.
As for records about what gallows etc are made out of, I suspect that there are detailed records, particularly from the 19th and 20th centuries when hanging became (an albeit grim) science of sorts.
Also, having read about the Hundred Years War and the detailed records made by civil servants in the 1300s, I would bet that quite old records exist about gallows somewhere, as someone would have built them and submitted a bill. Some things have changed surprisingly little in 800 years.
@zak - how do you have a forest? and how exactly would you have one that WASN'T tree laden???