1. The theory
In The Spirit of the Laws (1748), Montesquieu argued that liberty is safest when making the law, carrying it out and judging disputes are kept in separate hands: the legislature, the executive and the judiciary.
2. The United States
The US Constitution gives each branch its own article (I, II and III) and its own people: the President can't sit in Congress. Each branch can check the others, through the presidential veto, Senate confirmation of judges, impeachment and judicial review of legislation.
3. The United Kingdom
Government ministers sit in and answer to Parliament, which Bagehot called the "efficient secret" of the constitution: a fusion, not a separation, of executive and legislature. The judiciary, however, has become more clearly separate. The Constitutional Reform Act 2005 created the UK Supreme Court and moved the senior judges out of the House of Lords.
4. Evaluation
The statement is partly right: there is little separation between the executive and the legislature. But judicial independence is strong and growing, so a fair conclusion is that the UK has a partial, functional separation of powers rather than none.