The reason the public are backing her over Labour is simply because the leader of the Labour party is unelectable and astoundingly that's not just the public's opinion, a large majority Labour MPs think so too. As such there is no real opposition for those who want to remain in the EU to rally around which is why May is doing so well despite the lack of any coherent strategy for Brexit after 6 months.

If the UK had a decent Labour leader who, unlike Corbyn, was personally committed to remaining in the EU th UK might have a chance to stop the insanity before it goes too far. As it is I expect May will drag the UK into a Brexit nightmare of uncertainty and doubt for the next two years while her government fights internally over what they want from the negotiations before grabbing wildly at whatever is on offer before the deadline.