The United Kingdom is one of many developed countries in the world that does not have a 'written' Constitution.
The United Kingdom is unlike other nations in the world because it has not suffered any constitutional change since way back in the Middle Ages. It continues to be predominantly governed by a monarch in conjunction with the parliament. Having said that, the UK has proven to be of continuing success through the ages without a written form that many countries have adopted. But the UK has an unprecedented flexibility. It has effectively developed its own (non-binding) constitutional conventions to maintain their country is running smoothly. And, the bi-cameral (or dual chamber) parliament plus the required monarchical ratification serves to provide the comprehensive set of checks and balances which otherwise would be provided with a written constitution.
But the statement that the UK is without a constitution is very, very misleading. True, there is no written document, but the United Kingdom has a rich and diverse legal tapestry that works fluidly and it has done so for centuries, hundreds of years longer than the USA. This flexibility has given the UK the adaptation when necessary, and allowed the UK to flourish and develop where other countries didn't have a chance or come close.
Behind the scenes, however, is an equally strict and wrought-iron code of conduct, which often derives from codes of practices, Acts of Parliament and other 'bits and pieces' just as a written constitution would render. Thus there may not be an actual constitution present in the sense of a single definitive document, like the USA, but certainly the UK operates on the foundation of a 'constitution' that keeps the country running smoothly for centuries.
A significant aspect to the UK's 'constitution' relates to the legislative process required for legal enactment. Any bills must firstly be proposed to the House of Commons, an elected body of representatives empowered with legislative initiative power. The initial chamber proposes legislation then debates the provisions in depth, before agreeing on a final draft to pass to the second chamber, known as the House of Lords. The House of Lords are largely un-elected, with 'membership' passed down from generation to generation, or new members proposed from the House of Commons. They then have the right of veto, and the capability to refer back to the first chamber their proposed changes to any of the bills. This ensures no rushed legislation passes, and should cover all eventualities. After passing both Houses it is referred to the monarch, who has a personal responsibility to ensure any legislation is in accordance with using the will of the people, and is morally justified. Although the monarch hasn't used her power of veto since the 17th century, it is still a necessary constitutional safeguard in the UK for her or him to at least look at it.
The UK constitution may not be obvious initially, but there is most certainly an intricate web of governance and practice lying underneath its seemingly blank exterior. It continues to be the most successful 'constitution' in the world, and this is bolstered by its perpetual success and lack of problems since its early evolution.
Understanding of governance - UK Parliament