Show contempt with barely legal breaking rules, Downing Street initially ignores (10)
I believe the answer is:
disregards
'ignores' is the definition.
('disregard' can be a synonym of 'ignore')
'show contempt with barely legal breaking rules downing street initially' is the wordplay.
'show contempt' becomes 'dis' (I've seen this before).
'with barely legal breaking rules' becomes 'regar' (I am not sure about this - if you are sure you should believe this answer much more).
'initially' indicates taking the first letters.
The initial letters of 'downing street' is 'ds'.
'dis'+'regar'+'ds'='DISREGARDS'
(Other definitions for disregards that I've seen before include "Shows no interest in" , "skips" .)