Paul Scott:
Is there a suitable/cost effective way of LUL using the additional
spare platforms at Moorgate station once the Thameslink services
no longer use the branch?

"Bob":
Extend the DLR from Bank to Moorgate, Barbican and Farringdon.
Terminate at cross platform interchange on existing LUL carriage
sidings at Farringdon. Direct link from City Airport etc.

"Jonn":
Isn't the DLR at Bank a) too deep, b) facing the wrong way...

I wonder how bad it would be to make it a spiral tunnel, then?
Or a backwards S-shape, since DLR trains can make pretty sharp curves.

(Just musing, not a serious suggestion. If They seriously wanted
to do this extension, They'd ignore Paul's original suggestion and
build the connection to Barbican rather than Moorgate. Cf. Charing
Cross station, Jubilee Line.)

and c) blocked by the bank of England's vaults even if those two
problems could be overcome? ...

Well, I don't know where the vaults lie in relation to the DLR.