Cockney worker accepting dull job fast (8)
I believe the answer is:
Here is my best explanation:
'fast' is the definition.
(fast can mean secured)
'cockney worker accepting dull job' is the subsidiary indication.
I cannot really see how this works, but
'job' could be 'chore' ('chore' can be a synonym of 'job') and 'chore' is present in the answer.
The remaining letters 'and' is a valid word which might be clued in a way I don't understand.
This may be the basis of clue (or it may be nonsense).
(Other definitions for anchored that I've seen before include "Fixed in one place", "Secured a vessel to the seabed", "Ron ached (anag.)", "secure so?", "Held securely in place like ship", "In immovable position", "Made fast, secured", "Fixed firmly and securely", "Firmly fixed" and "With weight down, stuck in bed".)