The checks and balances that Grany can't see are provided by the lawmakers, (that is the whole of Parliament, which includes the House of lords as well as the House of Commons), the law recorders and dispensers (the justiciary) and the law enforcers ( the police forces)
These three organisations can and do keep the Executive governing body (The Prime Minister and the other Ministers of the Crownwho assist him) from becoming a one-man dictatorship.
When the Executive tries to limit the powers of any of the other branches, they are trying to upset the balance of power - in their favour of course.
This applies to wanting the final say when the justiciary have passed a verdict on an appeal, wanting to prorogue Parliament to stop them debating a Bill which the Executuve to pass, so that a deadline is crossed and it becomes law, and any other legislation that removes a power from another branch to give it to the Executive.
The general public don't see the erosion of the balance until it has become law and then by protesting against it they risk arrest.
Confrontational party politics and the whipping system lead to fights being about party advantage, not about what is best for the country and the diverse people in it.