The poll was legally binding, they had to leave.
Not that politics isn't broken ofc.
EDIT
I was wrong
There was no "will of the people". The people were undecided.
Whatever you can say about voting rights for overseas citizens in general elections, this vote was explicitly removing rights that they are currently exercising as part of EU membership — arguably they are the most affected by the outcome, yet were disenfranchised.
I may have missed something but at no point was anything resembling the current 'plan' ever put forward to be considered as 'the will of the people'.