The Highway Code isn't, in itself, law. However the policy of the Crown Prosecution Service is to take into account any breaches of the Code when deciding what charge, if any, to bring:
http://www.cps.gov.uk...n/pbd_policy.html#_32
While ABerrant correctly points to the Road Vehicles Lighting Regulations 1989, it's probably more likely that any prosecution would be under Section 3 of the Road Traffic Act 1988, which deals with 'driving without due consideration':
http://www.cps.gov.uk...s_of_bad_driving/#a16
Unless there were special circumstances, a court would be obliged to impose a penalty of between 3 and 9 points. (In practice that would almost certainly be just 3 points. There's actually the theoretical possibility of an immediate ban, possibly with the requirement to re-take a driving test, but the likelihood of such a penalty is effectively nil). The court can also impose a fine of up to £5000 (but the actual fine would normally be much lower, based upon the offender's income). There would also be a £15 'victim surcharge', plus court costs.
In practice, anyone stopped for driving with their fog lights on (when not required), would almost certainly be let off with a warning.
Chris