Firstly, I do second GBF's opinion that we have wonderful woods here in the UK. There are however situations where I see the use of small amounts of tropical hardwoods is justified, to provide an accent without having to use artificial colouring ( and I am not an enemy of colouring, it's just that some pieces call for natural colours).
With regards to the clearance of tropical forests, I do not think that even if all woodturners in the UK stopped buying tropical hardwoods it would make any difference at all. Where illegal logging is going, most of that wood goes into China for furniture, or is consumed locally for the same purpose (or for boat building or construction purposes). Illegal logging should not be confused with complete clearance, which is done to create space for farming, and in that case most likely the trees are just burned. Also, make no mistake: only a small percentage of trees in a tropical forest are actually valuable timber trees.
So if anyone wants to completely stop using tropical or exotic hardwoods to find peace of mind, go right ahead. Just don't delude yourself that it makes any difference to what happens all across South America, Sub-Saharan Africa or South East Asia.