like it or not, the Guardian is correct. The "democratic process" you talk about it is not what you think it is. Britain (why am I always having to point this out to British people?) is a parliamentary democracy. Parliament is sovereign. "The people" are not. Referenda are advisory and though MPs will give them due weight they are in no way obliged to follow them. Nor have they ever been required to do what the executive - in effect, the cabinet - tells them to do.
(This is not to say MPs are somehow above the democratic process: they are subject to removal every few years.)
In this instance, the public decided what they wanted but no mention was made in the terms of the poll, or by the shifty leaders of the Brexit campaign, of how it was to be done. This is what Parliament must now sort out. At present, it looks as if MPs have decided simply to let the prime minister do what she wants without question. That is a dereliction of their duty. It continues a weakening of the power of Parliament that goes back through the Blair years to those of Thatcher.
It intrigues me that those who claim to want to restore Britain's autonomy are also those who denounce judges as public enemies, threaten to abolish the House of Lords, and generally do away with the constitution that has kept the country running for the past several centuries.