Private health isn't exactly a competitor of the NHS though. It might be in some areas but it's generally a complementary activity. Consultants will often spend 30 hours a week dealing with ill people at the NHS then two evenings doing pointless but lucrative work for the worried well.
On the clawback point, this is a common blindspot in the public sector. I suggested to HR at HMRC that they put one in the contracts and they'd never heard of such a thing. Obviously i suggested that on my way out because i'm not completely dumb.
But clawbacks in the private sector aren't indefinite and the period is usually only two years. In my sector, they're fairly ineffective at the moment as the new employer will pick up the tab.
So long as there's no competition or negative effect on your output, my work and sector in general is fairly relaxed about second jobs. I can think of at least two close colleagues who have second jobs, on quite a small team.