A Labour MP told us Brexit will be 'catastrophic' if the UK doesn't get single market access
Dromey, who is MP for Birmingham Erdington and shadow minister for labour, told Business Insider that while he will not try and obstruct Britain's departure from the European Union, he has significant concerns about what the impact of failing to secure an adequate deal will be on Britain's economy - and on its national character.
"We have an obligation to stay true to the outcome of the referendum. It is therefore about the terms upon which Brexit happens at the next stages. I think there are some absolute fundamentals ... first, access to the European single market," Dromey, who supported Britain remaining in the European Union, said to BI.
"It would be catastrophic were we to have to fall back onto WTO [World Trade Organisation] rules with tariff barriers, which would see jobs lost on a grand scale on this country ... the idea is that you have such barriers is deeply damaging."
Britain's Prime Minister Theresa May installed a mixed cabinet of Brexit supporters and Remain campaigners when she took over from her predecessor David Cameron in July. She then promised that "Brexit means Brexit" and that she would trigger Article 50 by the end of March 2017.
However, she said that she would not give a "running commentary" on what a Brexit plan would look like or how negotiations with the EU would fare.
At the moment, those outside her inner circle can only speculate as to what Brexit would look like.
May has indicated that she intends to prioritise cutting immigration - a focus that may restrict Britain's access to the EU's Single Market, or force it to pay steeply for continued access.
May has also asserted that workers' rights - many of which are derived from European Union laws and directives - will be protected in a post-Brexit Britain.
But Dromey is not convinced.
He added: "I think there is a real risk of the gains of two generations being progressively lost, so that will be a huge focus for me."
It's not just economics.
Given Britain's reliance on migrant labour in sectors ranging from fruit-picking to health and medicine, the 68-year-old shadow minister for labour worries that May's focus on reducing "net migration to the tens of thousands ... would have a very significant impact on the economic success of Brexit Britain."
But that being said, it is not just an economic argument.
"This country is a strong, better, fairer country because of the successive waves [of immigrants] that have come to our shores. My dad came from County Cork to dig roads, my mum came from County Tipperary to train as a nurse. They worked hard all their lives, but both for their kids but also for their country," said Dromey.
The same is true for Brexit negotiations more broadly for Dromey.
"It's also about at the next stages, what sort of country do we want to become? Do we want to be a fractured, fearful, inward-looking country, or do we want to be the country that we should be, and a country that succeeds? We have got to put at the heart of Brexit Britain a continuing, strong relationship with Europe," he added.
Despite concerns, Dromey won't sabotage Brexit.
The government is currently appealing a High Court ruling that Parliament has to vote on the triggering of Article 50 - the formal process by which Britain will begin to exit the European Union.
Lib Dem leader Tim Farron says the party's eight MPs will vote against Article 50 unless a second referendum on the final terms of Britain's exit is guaranteed. Several Labour MPs also say they are planning to or considering to vote against it.
I asked if Dromey would also block triggering Article 50 if the government failed to secure any sufficient protections on single market access, workers rights, or immigration, would he vote down Article 50.
He said "no."
"I think [Labour MP] Keir Starmer's made it clear on our behalf that the referendum result has to be respected, and therefore we have to vote for Article 50. We cannot stand in the way of the invoking of Article 50. I think that would send entirely the wrong message. I think what we can do is fight very hard for the terms to be right thereafter," he concluded.