Low cloud allowed silence to envelop river bird (6,6)

'bird' is the definition.
(mistle thrush is a kind of bird)

'low cloud allowed silence to envelop river' is the wordplay.
I cannot quite see how this works, but
'cloud' could be 'mist' (mist is a kind of cloud) and 'mist' is found in the answer.
'allowed' could be 'let' (to let is to allow or permit) and 'let' is located in the answer.
'silence' could be 'sh' ('sh' is said to tell someone to be silent) and 'sh' is found within the answer.
'river' could be 'r' (abbreviation) and 'r' is present in the answer.
This explanation may well be incorrect...

Can you help me to learn more?