Bit of a misconception there, as London is bigger than LA (600+sq miles for London, 470-ish for LA) and more populated (8.2m for London, 3.8m for LA). You can, of course, start including the wider LA area but then you'd also be looking at including most of the south east of England to keep the comparison valid.If they keep building all over it, then sooner or later, the UK will end up like Los Angeles - one huge ugly sprawl!
As for looking like one ugly sprawl, this piece has a few flaws in it, IMO, but it still says that there is more woodland than "urban landscape" in England, and that's before any consideration that 3/4 of the "urban landscape" is greenery anyway.
So, if 80% of the current population can live in urban areas which takes up only about 3% of the land area, I think that it will take a while for your vision of ugly sprawl to become reality.
As for the OP, unfortunately, we need millions of new houses in this country. Whilst the natural response is to want them to be built in someone else's back yard, we're all going to have to face the reality that there is a logical flaw in that desire.