The space isn't the problem. It just means you can't use an off-the-shelf design.

Just like the UK, most towns and cities weren't designed for a mix of cars and low-speed traffic. They predate cars by quite a bit, so they are now pretty cramped. The average urban area in The Netherlands back in the 1960s-1970s looked very much like the UK does now.

Infrastructure has to be designed case-by-case, because no two neighborhoods are ever exactly the same. You might start out with a menu of a few dozen common designs, but they are always modified to fit the specific location. Often that means making compromises, but achieving 90% of your goals is already a lot better than 0%.

If it can be done in The Netherlands, there's no reason it can't be done in the UK as well.