British cooking takes a bit of skill with containers (7)

'containers' is the definition.
(basket is a kind of container)

'british cooking takes a bit of skill' is the wordplay.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'cooking' is an anagram indicator (cook can mean to falsify or distort).
'a bit of' says to take the initial letters.
The initial letter of 'skill' is 's'.
'takes' is an anagram of 'asket'.
'b'+'asket'+'s'='BASKETS'

'with' is the link.