Focusing on improving local and national transport networks, the report was published last year, but met with opposition from the Scottish Government due to transport being devolved.
Challenged on the issue at the Scottish Affairs committee in Westminster on Monday, Sir Peter insisted improving transport meant looking at all of the UK.
He said: “I was asked to look at the connectivity between the four nations of the UK
“I think some of those connections have been neglected because of the devolution of transport.
“Improvements in one country can make improvements in another.
“That seems to justify a proposition for looking at the whole network basic for public transport.
“I am reassured that what I concluded is very, very closely correlated with the strategic transport project review just published by the Scottish Government.
“It would be a different matter if somehow I had concluded something different.”
The proposals for Scotland include upgrades to the West Coast Main Line, increasing capacity and cutting journey times between Scotland and London, the Midlands and North West England, which are key for both communities and businesses.
Sir Peter told MPs it was “reasonable” for the UK Government to invest in Scotland.
He said: “The idea the UK could put funding into those parts of the network which it believed were of strategic importance to the United Kingdom seems to be quite a reasonable proposition.
"I don't think there's any difference between the map I’ve drawn of what the strategic transport network might be and the general views of the devolved administrations.”
Sir Peter was also asked about the so-called “Boris Bridge”, from Scotland to Northern Ireland, which his report claimed would cost in the region of £335 billion.
He said: “It’s obviously a huge job. Nobody knew how big, nobody had done that work before.
“It is possible to do it, but the time it would take and the sums of money are not credible at the moment.”