There are a number of ways you can search for your birth family (mother, father, brothers and sisters).

Go through your local Social Services for counselling.
Visit
https://www.direct.gov.uk/en/Governmentcitizensandrights/Registeringlifeevents/Birthandadoptionrecords/Adoptionrecords/index.htm/

You can use an agency to assist you, here are a few web sites that have been mentioned in the past.
https://www.baaf.org.uk/info/firstq/tracing.shtml
https://www.norcap.co.uk/
https://www.adoptionsearchreunion.org.uk/default.htm
https://www.ukbirth-adoptionregister.com/