The people in these cases are taking legal action against the police, and therefore ‘making claims against’ the police, under two different kinds of law: a parliamentary act – the Human Rights Act – and common law:

The Human Rights Act
The UK government, like other governments, signed a human rights convention – in this case the European Convention of Human Rights – which meant that the people affected’s rights were protected under international law (which forms part of UK law). The convention was later incorporated directly into UK law in the form of a Parliamentary Act – the Human Rights Act.
Read more about the claimant’s human rights claims here.

Common Law
Common law also forms part of UK law (alongside international law and parliamentary acts). Common law is formulated by Judges and cases. It often stems back many centuries and is not defined by statute (i.e. acts of parliament). These are principles that have been distilled by English courts through the ages into kind of “rights”. There are general principles that apply in common law (often replicated in Acts of Parliament now) such as fair trial, legality, property rights etc. They are a general set of legal principles applied by the courts.
Read more about the claimant’s common law claims here.