The leader of Plaid Cymru, Adam Price, has called for a trans-Wales railway to boost the country’s economy and culturally unite the north and south.

Sitting in a cramped two-carriage train trundling from Cardiff to Holyhead, Price expressed frustration that it was not possible to travel between south and north Wales by train without crossing into England.

He said improving rail routes in Wales could stop a brain drain of young people, and he suggested his country could become a test-bed for new rail technology such as hydrogen-powered trains.

The Guardian joined Price on the 9.21am from Cardiff Central as he headed north on the campaign trail. The train heads east to Newport and then north to Abergavenny. Before reaching Holyhead on Anglesey (Ynys Môn), it twice crosses into England and back into Wales, travelling through Herefordshire, Shropshire and Cheshire.

The journey – about 225 miles as the crow flies – takes four hours and 53 minutes, if running on time. On Friday it was already behind schedule by the time it reached Newport.

“Welcome to transport in Wales,” said Price, whose single ticket cost £88. “I’ve tried to scour the railway maps of Europe, I can’t think of any other country where you have to go into another country next door to travel from the south to north. It’s a unique Welsh experience. It’s extremely frustrating and we want to do something about it.

“Anyone who has ever tried to get around Wales by train knows that what we have now is a crumbling, 19th-century rail system that simply isn’t fit for purpose. We have about 5% of the UK’s population and yet we get just 1% of rail investment. We have cancelled electrification, and meanwhile the vanity project that is HS2 presses ahead. Never mind a high-speed rail link north to south, Wales doesn’t even have a low-speed rail link north to south.”

One of the most eye-catching policies in the Plaid manifesto is a £20bn green jobs revolution. As part of that, Plaid wants to reopen a stretch from Carmarthen, in south-west Wales, to the coastal town of Aberystwyth, in mid-Wales, that has been closed since 1965. Plaid envisages a second phase in which missing links between mid and north Wales would be filled in.

Price argued that a trans-Wales route would make communities such as Aberystwyth and Bangor, both thriving university towns, much more connected with the south and Cardiff. “A key problem in west Wales is the loss of young people from these communities. Investing in transport infrastructure such as the railways sends a message that you can stay here and still be connected to the world. You don’t need to be in central London, or central Cardiff for that matter, to have a successful business career.”

Price pointed out that there was no strong rail link between communities where the Welsh language is strong, in the north-west and south-west. “Those communities share a lot in common,” he said. “We have to make those connections to create a sense of a united country.”

A report commissioned by the Welsh government said reopening the Carmarthen to Aberystwyth line was feasible and would cost £775m.

Plaid’s manifesto spells out other rail plans, including creating a cross-rail for the valleys in south Wales and electrifying all major lines by 2030. Price said a silver lining for the rail industry in Wales was that decades of under-investment meant it was pretty much a blank slate.

“You’re starting from scratch in many ways, so instead of being behind the curve we could be at the leading edge, not playing catch-up but leap-frogging, thinking what the world is going to be like in 2050. There’s an opportunity for us to be a test-bed for technology such as hydrogen trains – an infrastructure laboratory for the 21st century.”