I'm unable to find anything definitive about the Club 55 being valid on the tube. However, the
FGW▸ website quotes the whole journey as one price and includes the tube journey. I would therefore be happy to assume that the tube is included.
Did you order any free
FCC▸ tickets? If so, it would be possible to do a Chippenham - London Club 55 for ^35, then ^1.90 (each way) on an
Oyster▸ card to Kings Cross where you could then travel for free on FCC.
With regards to the price from Melksham, I agree, the price difference is excessive due to Melksham being excluded from Club 55. Would two day singles plus the Chippenham ticket not work out cheaper?
Alternative - 57.00 super-off-peak return. I know this includes the tube, even though some train managers have told me in the past that it does not!
This should be printed with the Maltese Cross (i.e. +) before the route which means it is valid on the tube. I would hope (hope being the operative word!) that any train manager should understand what this symbol means!