Insincere support for the cheek of Labour? (10*)
I believe the answer is:
Here is my best explanation:
'insincere support' is the definition.
(I've seen this before)
'the cheek of labour?' is the subsidiary indication.
'the cheek' becomes 'lip' (lip is a kind of cheek).
'of labour?' becomes 'service' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'for' is the link.
(Other definitions for lip service that I've seen before include "It may be paid", "Insincere offer to assist", "insincere praise", "Insincere support", "Insincere praise", "Unreliable support", "The hypocrisy" and "getting no proper acknowledgment".)