Law and politics
Courts interpret the law in the context of particular cases. These courts are themselves an integral part of the law they interpret and how they interpret the law is part is the law itself. This goes by the name of Judicial interpretation or, more narrowly, Statutory interpretation.
There a multitude of different techniques for doing so; including the plain meaning rule (or strict constructionism as its called when applied to the US constitution) that your question is concerned with. This rule was explained in The Sussex Peerage Case (1844; 11 Cl&Fin 85):
Acts should be construed according to the intent of Parliament. If the words are clear no more can be done than to use their natural meaning. The words alone do declare the intention of the lawgiver.
If the words of the statute are in themselves precise and unambiguous, then no more can be necessary than to expound those words in their natural and ordinary sense. The words themselves alone do, in such case, best declare the intention of the lawgiver.
The limitations of this were illustrated in Whiteley v. Chappel (1868; LR 4 QB 147). A statute made it an offence 'to impersonate any person entitled to vote.' The defendant used the vote of a dead man. The statute relating to voting rights required a person to be living in order to be entitled to vote. The defendant was therefore acquitted.
The advantages of the literal rule are that it:
Restricts the role of the judge
Provides no scope for judges to use their own opinions or prejudices
Upholds the separation of powers
Recognises Parliament as the supreme law maker
The disadvantages are that it:
Can lead to injustice (see London and North Eastern Railway v Berriman  AC 278,
creates weird precedents which only a higher court or parliament can correct,
(wrongly) assumes that written English is plain, unambiguous and immutable in meaning over time,
it does little to dissuade the opinion of the public that the law is a ass as Dicken's Mr Bumble observed when told that the law supposed that he directed the activities of his wife.
Nevertheless, this is still the first port of call for a judge - assume the law says what it means and means what it says. Only if that leads you into absurdity, injustice, contradiction or thwarting the stated intent of parliament do you apply other rules of construction.
However, the law is self-correcting (to an extent) and a litigant unhappy with a judge's interpretation of the law can appeal and get other judges to decide if the first judge was correct or not. Failing that, faced with a string of cases with absurd or perverse outcomes, parliament can change the law; indeed, I have read more than one judgement (usually of appellate courts) where the judge(s) have explicitly called on parliament to do so.