What is your problem with a written constitution? What harm could it do? I'd agree that it does not, of itself, provide guarantees but it does set a benchmark. UDHR is not the same thing as a UK constitution.
Even your local bowling club has a written constitution. It is there to set standards and provide an agreed process to expel rogue members and committee members, including the president.
I agree with you about not voting greedy, anti-social, heartless fools into government, but that is a different issue. Our constitution could, for example, set an absolute limit on donations to political party, or do away with donations completely. Or take strict measures to de-couple the influence of lobbyists on parliament, or do away with an unelected second house, or provide direct, guaranteed funding for an independent press ( free speech, fair comment) regardless of who is in power and the political bias of each newspaper.