Would a written constitution be beneficial to the United Kingdom?

The implementation of a completely codified constitution to replace our currently uncodified constitution would result in the creation of a singular enshrined document. It is important to distinguish that our current constitution is written, not in one place but written down in statutes or legal decisions otherwise known as common law. A written constitution could be worse for British democracy since the judicial hierarchy could abuse their power. Furthermore the Supreme Court judges could interpret the written law to suit their own political bias. An issue created by a completely written constitution is the subsequent erosion of parliamentary sovereignty. In this way it would create unrest since it would be seen as a challenge or threat to their legitimacy. Therefore a written constitution would be a poor choice for Britain since the limitation of governmental power could be negative. Moreover, it would soon be rendered anachronistic because it is only contextually relevant, as with America’s constitution formed in 1787 by America’s founding fathers which is hardly adaptable. An uncodified constitution is better since the Prime Minister can respond quickly to emergency situations in current affairs, resulting in it being a progressive process. A written constitution would certainly not be a better form of constitution for Britain since it is easily made anachronistic, is susceptible to judicial tyranny, would undermine parliamentary sovereignty and the Human Rights Act still takes precedence over our current uncodified constitution which works well as a flexible written law.