He quite reasonably asks where TfL will find the £310 million from to
buy Tube Lines, given that TfL said they were going to struggle
finding the £400 or so million for the Tube Lines funding gap (as
determined by the PPP arbiter).

Surely TfL weren't expected to pay the £4.46bn upfront for a 7 year
programme! The £400m shortfall was on top of the £4bn TfL had budgeted
and were willing to pay for the infrastructure works. Surely the £310m
would simply come from this years payment to Tubelines for their work,
AIUI.