Far from impossible. I believe version were considered at least three times as far back as the first half of the 1800's. You need a person better with British details to give you the list.
And generally, it fell apart on the same issue. It was not creating lesser parliaments with lesser powers for Ireland, NZ or whatever. The issue was demoting the English parliament to one of many parliaments. And then there is the issue of the House of Lords. The English imperial system greatly benefited the English elite which were mostly near London.
But since it was seriously considered at times by at least some important politicians, then it was easily possible. You just need something to make the loss of power by the English elites to be outweighed by something else. You need a threat to the British Empire that is serious enough and long lasting enough for reforms to occur. So handwavium, France or German dominate Europe after some wars or series of wars. England lacks the funding/manpower to have a large enough army and navy to counter the threat. Given the right other factors, a imperial federation could arise.
We should also not minimize how much power England is losing. Even without House of Lords reform and white only sufferage, we can easily see England consistently outvoted on issues. In many ways, the British Empire faced the same dilemma the Roman empire faced, but chose a different path. Rome chose to expand citizenship and let non-Roman rise to the top. England chose to keep the power in English (London) hands. This is one of the many reasons Rome lasted so much longer than London as a power center. The glory of the British Empire is really only about 150 years. Rome is 500 plus depending on how you count things.