Busy road to boast street cook (9)
I believe the answer is:
microwave
'cook' is the definition.
(microwaving is a kind of cooking)
'busy road to boast street' is the wordplay.
'busy road' becomes 'mi' (resembles M1, English motorway).
'to boast' becomes 'crow' (crowing is a kind of boasting).
'street' becomes 'ave' (abbreviation for Avenue).
'mi'+'crow'+'ave'='MICROWAVE'
(Other definitions for microwave that I've seen before include "Fast oven" , "Cook" , "Kind of oven" , "(Kitchen) oven" , "Kitchen appliance" .)