Trust in democracy
The security and validity of the voting system is essential (in the truest sense of the word) to democracy. You can't improve on that with e-voting, in any way whatsoever, because any systemic problems with managing paper systems will be X times worse for e-voting.
What e-voting could be good for is not replacing paper, but supplementing it - so we can have more democratic input, with more fine-grained feedback on specific issues. For just one example, you could have a paper ballot election that elects a government, and a parallel e-vote that tells the government what people actually liked or disliked about their manifesto (and that of other parties).
And for anyone pointing to the problems we've had with referenda: that's as much as anything because UK democracy is too weak (in various ways), feedback too infrequent, so those referenda become about other issues than what's on the paper. Any use of e-voting should beware of running into that effect.
