The separations of power can be witnessed in the following, tenure of office, judicial immunity from suit, immunity from parliamentary criticism and judicial review.
In Tenure of office all judges in the Supreme Court with the exception of the Lord Chancellor hold office during good behaviour, and is only subject to the Act of Settlement 1700, removal by the monarch on address presented by both Houses of Parliament. However this has never resulted. But the Lord Chancellor has recently outlined new measures to investigate serious allegations made about Circuit judges downwards. This can only be exercised by the Lord Chief Justice after an investigation into these allegation by a senior judge appointed by the Lord Chief Justice, then with further discussion and agreement of the Lord Chief Justice and other senior judges.
Judicial immunity from suit means no judge can be sued for anything done in his or her judicial role. This enables them to remain independent and they are put under less pressure, thus will have less of an effect on their decision-making. However Lord Denning at age of 83 in 1982 was threatened by legal action against him for libel by two black jurors. This was following remarks he made criticising the two black jurors, who were involved in a riot trial in Bristol. This led to Lord Denning apologising and announcing his retirement.
Judges also have immunity from parliamentary criticism. Which means no individual judge can be criticised in both Houses of Parliament, except by a way of substantive motion (very uncommon). This measure is designed to prevent politicians interfering with the judicial system. But this prevention also applies to any full time judge, so they are excluded from the House of Commons and not interfering with politics. This partly applies to the Law Lords, Master of the Rolls (all Life Peers), meaning they are excluded from political debates in the House of Lords.
The checks and balances part of judicial independence comes into effect in judicial reviews. Where judges are required to examine the legality or procedural correctness of government decisions. In many circumstances government ministers have their decisions overruled.
Judicial independence is also important when judges chair inquiries into major national events that are of relevance to the whole nation. For example there were inquiries into the Hillsborough disaster and Dunblane shooting.
Montiquieu’s principle of Judicial Independence is not only adopted by Britain it also adopted by the United States of America.