// If all they campaigned on was Remain and Brexit it might be said that it was a strong indicator that people wanted to remain. However, regardless of this omnishambles no party, including the Brexit party, would campaign solely on that. //
Flipping the premise of the question, if a party such as Boris Johnson's "Do or Die" Tories and/or the Brexit Party won (big) in the election, I'm pretty sure they would see it as a mandate for forcing through either a deal or an immediate exit without a deal by the end of October. So I don't think it would be unreasonable for a Remain-leaning party to see their own victory as a mandate for, if not remaining without further consultation, then certainly a softer stance on Brexit.
The situation is further complicated by the fact that Labour under Corbyn is not anti-Brexit but anti-Tory. Leaving aside the obvious nonsense that any deal they'd bring back would be "brilliant", that's still Corbyn's strategy. Negotiate their own deal, offer it to the people, and presumably feel smug about it all.