Tricky one, OP,
Feel so sorry for him (and every other kid in similar situation).
Kids being kids, getting scruffy and dirty through having fun without fear of ruining immaculate clothes, having otherwise great parents whose housekeeping approach just happens to be different etc....all positives.
Permanently smelling so noticeably bad and other kids avoiding visiting his house, though, already make him very vulnerable to isolation/ bullying.
At age 10, the poor lad probably feels utterly humiliated, and I expect is only too aware. The "sweet, polite and happy" demeanour might well be masking his true feelings, in order to compensate and thus feel accepted by at least you and your DC.
Obviously this is total conjecture and could be far, far wide of the mark, but two things occur to me:
- If you've chatted with/ spent time at the beach with his Dad, presumably you haven't noticed any similar hygiene/ unwashed clothes issues with him?
Because a filthy house smell (as in warranting serious, constant concerns, not simply different standards of housework or occasional lapses due to illness/ long working hours/ different priorities etc.) tends to permeate everything.
(Once saw at first-hand someone caught in a vicious cycle of tight finances, minor debt, no insurance > stress and other issues > prevented broken washing machine repair > no drier > not able to afford laundrette (or transport there) > overwhelmed by handwashing laundry, so was infrequently done > inadequate heating and only sporadically hot water > damp house > air-dried clothes already smelling mildewy, musty etc. etc.).
So that would imply that the adult here somehow manages to keep himself/ his clothes within a 'normal' range. Assume same with mother? Perhaps only when they're working outside the home, or in the company of non-family members, though.
A kid wouldn't necessarily have the knowledge, means, inclination. If neither parent indicate otherwise then that's become his norm.
- Some kids just hate the palaver of personal hygiene. His age makes close supervision and parental enforcing of hygiene less likely (especially if they're slacking in that area themselves)...evidence of damp hair and sounds of bathing doesn't always equate to thorough soaping. (It became apparent to a friend that her 11yr DS's 'shower/ hair washing/ teeth brushing' was only a cursory rinse in plain tepid water.).
Deliberately withholding access to clean clothes and baths, on the other hand, is a well-known method of control and abusive behaviour.
Sexual abuse can also be behind children avoiding baths, in extreme cases. Seeing themselves naked and having to touch their own bodies is traumatic, and their hope is that dirt/ smell repels the abuser. Tragic 
Agree with PPs...well done for seeking advice from NSPCC.
Professionals would always rather well-meaning members of the public reported, rather than let it go through worry of being deemed interfering. That child's adolescence could turn out a lot happier.