Find a Solicitor (https://solicitors.lawsociety.org.uk/) is owned by the Law Society of England and Wales. Find a Solicitor is a free service for anyone looking for information about organisations or people providing legal services in England and Wales that are regulated by the Solicitors Regulation Authority (SRA).
Alternatively the Ministry of Justice (MoJ) offer a search facility to find a legal aid adviser or family mediator.
Find a Solicitor aims to include all SRA regulated law firms, individuals and the organisations that contain regulated individuals who choose to be listed. Additionally, it references non-solicitors who are members of the Law Society’s accreditations. For example, the Family Mediation accreditation is open to qualified mediators who may not be regulated by the SRA. They are still, however, required to satisfy all entry criteria before being granted the Law Society’s accreditation.
A notary is a specialist lawyer, you can search all notaries entitled to practice at find a Notary
The principal role of a notary in England and Wales is to “attest the authenticity” of deeds and other legal documents for use abroad.