The call at Westminster came as the Government was again pressed over the future of the £43 billion Northern Powerhouse Rail (NPR) scheme, also known as HS3, aimed at connecting cities in the region on an east-west route.
It follows reports the scheme, a key part of Boris Johnson's "levelling up" agenda aimed at spreading prosperity in the North and shoring up support in the party's "Red Wall" streets, could be scaled back.
The Yorkshire Post has previously seen government documents which suggest that rather than building a new high speed rail line between Leeds and Manchester, the project could now follow the route of the existing Trans-Pennine line through Huddersfield and Dewsbury.
Northern leaders fear that the high speed route may now not include a station in Bradford city centre, something considered vital for the city's economic fortunes.
Meanwhile, Mr Johnson has promised a national flagship to succeed the Royal Yacht Britannia.
The vessel could reportedly cost £200 million to build and is designed to support diplomatic, trade and economic relations as part of the Prime Minister's vision for post-Brexit Britain.
Pressed in Parliament for a commitment to the rail project, Transport Minister Baroness Vere of Norbiton repeated the Government was considering "all options" as part of an integrated rail plan and said NPR was "a very important part of that".
Criticising the lack of detail on progressing the scheme, Labour frontbencher Lord Rosser said: "Can she at least assure us that work on the construction of Northern Powerhouse Rail will take priority over the start of work on the Prime Minister's latest project - the construction of a new royal yacht?"
Lady Vere said: "I reiterate that the integrated rail plan must come first. Without it, it is pointless having a plan for Northern Powerhouse Rail because, of course, the whole point is that everything has to be integrated."
The exchange came as the Government was tackled over the rejection of proposals for an underground "hover train" network linking northern cities.
The maglev - magnetic levitation - system uses strong electromagnets to lift and propel the vehicle above the track.
Lady Vere said the Government had "thoroughly investigated" the concept for the North, but added: "We concluded that rail remains the best option for a number of reasons, the most important being that new conventional rail infrastructure can better be integrated into the existing network."
Pressing the minister, Tory peer Lord Moylan, who served as a transport adviser to Mr Johnson when he was London mayor, said: "Maglev is a great British invention increasingly deployed in Asia for high-speed travel. As our world-beating British tunnelling engineers have shown, constructing railways in-tunnel can be cheaper than constructing them on the surface, provided that it stays in-tunnel.
"However, it seems that every proposal for maglev that comes from the Department for Transport is rebuffed.
"Can the minister explain why her department is so wedded to a 200 year-old technology that, when constructed on the surface, can both cost more and be very annoying for local voters?"
Lady Vere said: "We must look at all technologies, and that is precisely what we do. He makes an important point in saying that systems around the world use this, but just one operational high-speed system does so at the moment - the Shanghai City maglev.
"There are many others operating at lower speeds, that is less than 100 mph, and obviously, there is one in construction in Japan, but it is coming up against some cost pressures."
Lord Kirkhope of Harrogate said: "My noble friend’s idea of an underground magnetic railway between northern cities certainly has a strong attraction, especially following Elon Musk’s proposal for 1,000 mph trains in the United States, and especially coming from a former deputy chair of Transport for London.
"However, as Transport for the North has said, our aims in the North should be to improve the frequency, capacity, speed and resilience of our transport system."
And Labour peer Lord Berkeley said the Minister was right about the Shanghai maglev, "which I have been on".
He added: "It is very fast and very noisy, but the technology, and therefore the costs, are very tight, because the track has to be kept within plus or minus half a millimetre in both directions, vertical and horizontal."