Road closures are generally brought about by the local council making a temporary traffic regulation order (TTRO) or temporary traffic regulation notice (TTRN). Some info is provided
here.
A road closure TTRO or TTRN does not usually suspend any speed or parking regulation orders and therefore they remain in effect despite the road closure.
If the TTRO or TTRN prohibits driving (accessing) or parking on the closed road, it is an offence to do so under
s.16(1) RTRA 1984. How the offence is enforced depends on the offence. Driving is likely to be enforceable by the Police and parking by the local council. The Police may consider ignoring the road closed sign as careless and inconsiderate driving which is an offence under
s.3 Road Traffic Act 1988 (especially if road workmen are inconvenienced or endangered).
