Apparently there are several options. The most obvious and easiest is for the UK to reverse its position on Article 50 of the EU charter and simply end the whole Brexit effort. That would mean that the whole exercise ends immediately.
The other options will take more time and require Britain to ask the EU for an extension for its Brexit beyond March 29. What will be the reaction by Brussels is not clear, but the EU most likely would grant an extension.
Another option is for the Prime Minister to step down from her position and for the country to call new general elections. That would mean a fairly long drawn out process of campaigns and electioneering with no certain outcome. If that were to happen, Brexit would probably be back at square one.
Then, there is the possibility for Britain to call another referendum on Brexit. That, too, would take quite some time with an uncertain outcome, despite the overwhelming “No” vote in Parliament.
Finally there is the option for renegotiations with Brussels. That would require for Prime Minister May to be able to hold on to her position or for a new prime minister to take the stage with the objective of Britain leaving the EU. Since it has taken two years to get to this stage, another round of talks would take at least that long and the outcome is as uncertain as another referendum.
There is one positive impact Parliament’s rejection of Brexit should have on the rest of Europe is that the various stirrings of a departure from the EU should now be put to rest. The most obvious one is Catalonia’s effort to leave its union with Spain. It is unlikely that Barcelona will again push for devolution. The same thing is true for Scotland. Even though PM Nicola Sturgeon has made noises of calling for a referendum on devolution, the likelihood of such an event now is greatly diminished.
Much will depend on whether PM May will be able to weather efforts to oust her from the Prime Minister position and what happens next. If she is ousted, will Labor take over and will that mean that the new PM will take up the cause for Brexit? Probably not. If she stays, how will she proceed? Will she keep battling for Brexit?