Wild pea in mushy plant found on sandy shores (3,5)

I believe the answer is:

sea poppy

I'm a little stuck... Click here to teach me more about this clue!

'plant found on sandy shores' is the definition.
The definition and answer can be both plants as well as being singular nouns.
Maybe there's a link between them I don't understand?

'wild pea in mushy' is the wordplay.
'wild' indicates an anagram.
'in' indicates putting letters inside.
'mushy' becomes 'soppy' (I've seen this before).
'pea' is an anagram of 'eap'.
'eap' put into 'soppy' is 'SEA POPPY'.

Can you help me to learn more?

I've seen this clue in The Hindu.

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