if you married outside the UK and your wife has a settlement visa, your wife can work soon as she lands in the UK, but as mrshark says it could be wiser to get a NI number first or she will probably be paying too much tax and the chances of getting a job from an employer might increase if she already has one.
if your wife came on a fiancée visa, she cannot work til your married and she has FLR.
yes i had a few problems when my misses got a job working for the NHS, they wanted to see my passport to
you shouldn't really have a problem, some people have a few problems if their settlement visa is expiring soon and they haven't got ILR yet, (employer might be worried they will not get ILR and they face possibility of a £10k fine) but i think most people don't really have a problem.
the employer can check with UKBA that your wife has the right to work online.
