It's neither possible nor desirable to ignore Parliament in this matter. Forcing through the sort of exit OG wants in the manner he desires (ie, government bypassing Parliament) will simply not happen, unless the party in question wants to destroy itself and the country with it.
Still, having ruled that out, I have no real idea what will actually happen next. The most likely outcome, I think, is that Parliament ends up capitulating to the inevitable and voting through the Withdrawal Agreement in more or less its current form, but with the proviso that the question be put to the people for a second referendum.