At the Belfast Self Build show, I came across this outdoor de-greener for dealing with algae and moss on HARD surfaces. It is non toxic, non corrosive, chlorine free, colourless and odourless and may be worth trying on thatched roofs.
When I spoke to the people they had no experience of treating thatched roofs, which is not surprising given the comparative rarity of them. So when it comes to Algae in Thatching, it has yet to be tested.
If you fancy trying out, the website is www.algaeprevention.co.uk.
Let us know if it works.