Clue: Random policemen turning up to house heading to room with a detective (8)
Answer: SPORADIC
Explanation: Definition: Random
An envelope ('to house') of R ('heading to **R**oom') plus 'a' plus DI ('detective' inspector) in SPOC, a reversal ('turning up' in a down light) of COPS ('policemen'). I arrived at the answer on the basis of CID ('policemen turning up'), which turned out to be totally spurious.