The procedures on starting a claim are covered within Part 7 and Practice Direction 7A (PD7A) of the Civil Procedure Rules.
PD7A, at paragraph 3.1, states:
A claimant must use form N1 to start a claim under Part 7.
And at paragraph 2.11(1):
The normal rules apply in deciding in which court and specialist list a claim that includes issues under the Human Rights Act 1998 should be started. They also apply in deciding which procedure to use to start the claim;
There are a number of provisions and variations at PD7A (from para 2.1 to 2.11), but if the value of the claim is less than £10,000 one can submit it using Money Claim On Line MCOL.
Or, one can post Claim Form N1 to the County Court, remembering to answer the question on page 2:
Does, or will, your claim include any issues under the Human Rights Act 1998?