The press release says that the TOCs will be no better or worse off
under the new system - which must mean the average fare remains the same.

(From the release: "[...] London commuters will on average pay no more
using the new zonal fares than they would had current fares continued an
been increased as permitted by regulation. Operators will not make a net
gain from the change in these fares.")

I read that and felt the wording a little suspect and whether the
suggestion was any difference one way or the other would be funded by the
GLA.

If that were the case, the GLA would win either way, any shortfall funded
by the London council tax payer and any surplus spent on other stuff ...

D