Well Grozney - I think you'd find that most therapists are okay with bodies - we've seen and felt enough anyway. The issue is nakedness, and whether or not boundaries are crossed. The draping, or the underwear sets up a boundary that permits both parties to know where things stand. It's a measure of protection for both parties.
I've had situations where like AngelFish, I've tried to tuck a towel in, only to find nothing to tuck it under! Which shows you how we don't really care - just that in that situation, it means we have to be more careful how we drape.
As you know, in the US, states that regulate massage (38 of them) require draping by law. In the UK, there is no such legislation, so it really is a matter between you and the therapist. If you do not want a towel, you could bring a sheet along for draping - that works, and is less heavy. (I wouldn't recommend silk or satin - one, that reveals all, two, they have a tendency to slip off! [])
I personally, would wear nothing under the drape when I am with a masseuer, but with a masseuse, I would. Just because I do not really want to offend someone's sensibilities. Most blokes have showered together in schools and college, so it's not that big a deal.