"But UKIP only have two policies. One published - get out of the EU - and one that Nigel Farrage 'let' the papers have - restore grammar schools.
Other than that they don't have any.
So why on earth would people would vote for them?"
Because it is not about policies. The public doesn't know many of their policies and frankly doesn't care because as you say
"All about the 'problems' but nothing whatsoever about what UKIP would do to 'solve' them."
But there is only one thing that the public wants "solving" and that is it wants to teach the establishment parties a lesson because the main problem that the public wants solved is that the establishment parties have all, bar none, let them down and not listened to them, and the more that the establishment and its mouthpieces accuse UKIP, and by extension, the public who are voting for them in huge numbers now, of racism and so on, the more that confirms to the public that the establishment is not with the people and that it is against the people and holds them in contempt, just as it holds UKIP in contempt.
The public want problems solved, but they have got to the point where they no longer believe that the establishment parties can solve the problems and now even think that the establishment parties have become the problem.
The public does not know how the peoblems will be solved, but ot no longer believes the establishment will or even really wants to solve what the public consider to be the problems.