Without source, fop twice claiming party's leader is BBC puppet (4,5)
I believe the answer is:
andy pandy
'bbc puppet' is the definition.
I don't know anything about this answer so I can't tell whether this works.
'without source fop twice claiming party's leader' is the wordplay.
'without source' means to remove the first letter.
'fop' becomes 'dandy' (synonyms).
'twice' indicates the doubling of some letters.
'claiming' is an insertion indicator.
'party's leader' becomes 'p' (I can't explain this - if you can you should give a lot more credence to this answer).
'dandy' with its initial letter taken away is 'andy'.
'andy' duplicated is 'andyandy'.
'andyandy' going around 'p' is 'ANDY-PANDY'.
'is' is the link.
Can you help me to learn more?
(Another definition for andy pandy that I've seen is " TV character".)