The comment about new trains and old signalling is a bit weird, since on the Piccadilly they’re just adjusting signal positions so they can see them clearly from the new train cabs.
That said, there is a signal control upgrade in progress on the Bakerloo which will likely provide a little bit of uplift potential. On the Piccadilly they are planning to run 27tph with manual signals once they have the new rolling stock, since that has had the same control system upgrade a few years ago. That is getting to the limit of the signalling though.