Which of those rights did people in this country not have prior to the HRA being introduced? Sorry but I believe that there are too many people that are happy to break the law all their lives but then expect the law to protect them when it suits them. The rights of the law-abiding have to take precedence over the rights of criminals where there is a conflict between the two.
Actually, we had all of them, because we had subscribed to the European Convention on Human Rights. However, the British Parliament decided that it wanted to enact the HRA under domestic legislation so that we ourselves can control the way in which the rights are interpreted rather than leaving it up to Strasbourg. This seems to have worked well - for example, the recent case in which Liberty intervened to stop a paedophile from taking home nude (but not pornographic) photos of his victim which were on his computer, citing Article 8 - the little girl's right to privacy.
The rights of the law abiding DO take precedence. There are only three articles which are "absolute" - right to life, freedom from torture and right to a fair trial. These apply to everybody, all the time, and quite right too. This is a civilised country and we do not employ extrajudicial executions, torture or show trials no matter how criminal the person might be.
The rest of them are "limited" rights. The government can interfere with them, but only if it is necessary in a democratic society in the interests of national security, public safety or the economic well-being of the country, for the prevention of disorder or crime, for the protection of health or morals, or for the protection of the rights and freedoms of others. (That is from Article 8 but the others are broadly similar.)
So for example, criminals can be put in prison, which is a breach of Article 5 (right to liberty) but this is necessary in the interests of public safety etc. Freedom of expression is guaranteed but not the right to shout fire in a crowded theatre or racial abuse at minorities, because that interference is necessary for protection of others.
People who clamour to repeal the HRA usually don't understand what it is.