Luckily cleaning the tubes was easy. I didn't want to use any chemicals because the roof is part of our rainwater system collection area. Instead I just wiped them clean with a micro-fibre cloth labelled 'glass', rinsing it frequently in a couple of buckets. The closest three tubes in the photo below have been cleaned. The whole operation took about 20 minutes.
No measure was made of how much improvement was gained by cleaning the tubes but after I finished I watched with satisfaction as the controller showed the system continuously heating the circulating water by about 10 degrees as it passes through the manifold. Hooray for showering in solar heated rainwater!