Having your fundamental democratic rights written in a form that is well protected and defended is a valuable thing. It holds the government accountable, it might not always seem like it but there is some barrier against abuse.
It also makes it harder to push through significant legislative changes, which is a good thing when (like with healthcare) it has a huge impact.
In the UK we're not even citizens but subjects, beholden to the monarch and her government. Trial by jury has been abolished for certain crimes, you can be incarcerated for up to 90 days without charge ,along with a thousand other erosions of civil liberty.
This is a separate debate, but what the fuck.
Firstly, America's constitution didn't stop Guantánamo Bay. Britain's anti-terrorism laws are weak in comparison.
Secondly, the UK has a massively complicated constitution, and codifying it would take a huge amount of time and resources, over simplify it, and would probably never get finished due to all the debate there would have to be about every little detail.
"In the UK we're not even citizens but subjects, beholden to the monarch and her government" What difference does that make?
"Trial by jury has been abolished for certain crimes" That's because its pointless for every little thing and wastes peoples time. Just because some crimes don't use a jury doesn't mean the trial is worse. Often a judge(who is properly scrutinised and well trained) can make a far better decision than a jury who just want to go home and get on with their lives.
There hasn't been a change to the American constitution for almost a hundred years. Unlike them we're not hidebound by history.
This is just my opinion, you can argue either way