The discussion comes after Mrs. May suffered a defeat on April 18, as the House of Lords voted against leaving the customs union following Britan's departure from the European bloc.
Former culture minister Ed Vaizey, sacked by Theresa May in 2016 and a member of her Conservative Party, addressed the small number of MPs scattered sparsely in chamber.
He said he is learning more and more about Brexit every day, with a hint of sarcasm.
"I've learnt that there is no longer going to be a bonfire of regulations from the EU — that it's actually all right, we are going to adopt all of the EU regulations. I've learnt we are not trading enough with the EU, so we are going to make it even more difficult to trade with the EU and I've heard that the Good Friday agreement is a waste of time and we're going to have a hard border with Northern Ireland because of Brexit."
Vaizey was one of the ministers in 2015 who said he was worried about the state of the Conservative party under May's leadership.
Another Tory member, Sheryll Murray MP, however, questioned the cost of staying in the customs union.
"No doubt we will still have the divorce bill but on top of that we could possibly, if people voted for a customs union, see an annual bill for effectively staying in."
She added there could be no worse deal where Britain effectively stays in the EU and still has all the costs and no say over it.
"It is a massive betrayal of the British people who voted to leave," Sheryll Murray MP concluded.
Theresa May finds herself between the rock and the hard place on the matter of the customs union, as pro-Brexit officials suggest a "customs partnership" arrangement to replace the current set up. On the other hand, the EU supporters argue that the only way to avoid a hard border in Northern Ireland is to stay in the customs union.
Further discord among the Conservative party members was revealed as Antoinette Sandbach Tory MP said her vote is determined by her constituents' interests that would be hurt in case a European Economic Area (EEA) style agreement is not struck.
"The importance of pharmaceuticals, car manufacturing, food manufacturing, the energy sector and the nuclear sector to the north-west is absolutely clear. The government's own analysis shows that if we don't have an EEA style agreement that there will be a reduction of 12 percent in the GDP growth in the north-west."
A free trade agreement with the EU is crucial for the sector and consumers. Read our report on the impact of Brexit on the processed food and drink sector: https://t.co/iP4hzWca1A pic.twitter.com/ZirHhqpn5x— Business, Energy and Industrial Strategy Committee (@CommonsBEIS) April 26, 2018
Simon Clarke MP of the Conservative party painted a dark picture of Britain's future as a member of the customs union, post Brexit, referring to Turkey's case.
"The only large country which has a customs union with the EU, but which is not an EU member state — is Turkey. But Turkey's customs union is almost unbelievably asymmetrical. The EU doesn't need Turkey's consent to enter free trade agreement with other countries and Turkey is obliged to reduce its tariffs with that country. However, the third country, with whom the EU enters the FDA, is under no reciprocal obligation to open its own markets to Turkish exporters. In other words, Turkey has to open her markets but may not reap any benefits. "
The economic consequences of leaving the EU customs union and the complexity of potential establishment of a hard border between Belfast and Dublin, has been at the heart of the Brexit deal debate. So far, no clear plan on the resolution of the problem has been presented by the government.