This claim just isn't true. The English Civil Wars (also sometimes called the English Revolution) are a prime example: the deposing of Charles I, the execution of the king, the rise of Cromwell's protectorate, the advent of written constitutions in English government, and finally the restoration of the monarchy after the death of Cromwell. Here is an old AMA hosted on this sub on the English Revolution.

There is also the so-called "Glorious Revolution" about which I know considerably less. Here is an AMA on this sub with an expert on the Glorious Revolution.

This claim in incredibly factually inaccurate. Even if you exclude the rebellions and uprisings in its colonies, Britain has had many wars of internal conflict. Also, where are you getting this idea that "Britain" has existed as a country for 3,000 years? This is terribly untrue. Britain was only united as "Grewt Britain" as recently as 1707, with the Act of Union. This act came after many periods of war in the centuries that preceded it.

As /u/White___Velvet pointed out, the English Civil War and the Glorious Revolution rocked the 17th century. Before that, you had wars like Rough Wooing in the 16th century, or the war of roses in the 15th century. Before that, you had the Wars of Scottish independence in the 12th and 13th centuries. This is also just a sampling of the conflicts that British states waged against each over over the last several centuries.