Searching for birth parents can be a difficult task. There are some resources available online that can offer valuable advice for those wishing to find more information about their birth parents. Formal adoption records did not exist prior to 1927, as a result there is minimal documentation from before this period.
The National Archives do not hold adoption records themselves, but they have several links to organisations that do, searching for birth parents (i.e. adopted / fostered / abandoned children's searches): https://www.gov.uk/adoption-records/accessing-your-birth-records
British citizens can sign up to the Adoption Contact Register and can access your adopted birth records: https://www.gov.uk/adoption-records/accessing-your-birth-records
WikiTree Adoption Angels are volunteer genealogists who want to help adoptees, for free: https://www.wikitree.com/wiki/Project:Adoption_Angels
Adopted.com allows users to reunite with lost family members. However, to message other users requires a paid subscription. Matching with others is free: https://www.adopted.com