Quinoa, unlike Amaranth, likes cool summers, so it should grow fine in the UK. There are some new selections that are bred to grow in the Pacific Northwest of the United States, which is a maritime climate similar to much of the UK. You should start it about now, direct sowing where it is to grow, then thin to the desired spacing after it's well up and growing. It likes loamy soil in full sun with a neutral pH.
Some cultivation information for Quinoa...
Here are some varieties currently being grown or tested in the PNW. We will be growing Brightest Brilliant Quinoa this coming season here in western Washington state.