Pains reportedly following stone cold items eaten at teatime (4,5)

I believe the answer is:

rock cakes

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

'cold items eaten at teatime' is the definition.
(rock cakes might be eaten for tea)

'pains reportedly following stone' is the wordplay.
'pains reportedly' becomes 'cakes' (I can't explain this - if you can you should believe this answer much more).
'following' means one lot of letters go next to another.
'stone' becomes 'rock' (synonyms).
'cakes' after 'rock' is 'ROCK-CAKES'.

Can you help me to learn more?

I've seen this clue in The Telegraph.

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