You have several elected representatives at different levels of government.
Your Handsworth councillor represents you on Birmingham City Council. The Metropolitan District Council is responsible for all aspects of local services and policy, including planning, transport, roads (except trunk roads and motorways), public rights of way, education, social services and libraries. Most councillors are not paid a salary, but get a basic allowance for the work they do.
Your Birmingham, Perry Barr MP represents you in the House of Commons. The House of Commons is responsible for making laws in the UK and for overall scrutiny of all aspects of government.
Lords are not elected by you, but they still get to vote in Parliament just like your MP. You may want to write to a Lord (more info).