Lots and lots of children were abandoned in London at the time. What occurred is they would usually be handed over to an orphanage and become a ward of the state, from then on your story is basically the same as "Oliver Twist." depending on the quality of the orphanage you ended up in (There was a good chance at the time it was poor quality.

Your food and education may come from a Ragged House, basically a free school for poor children. Upon reaching the age of 13, you were usually sent to work. Some orphanages were created solely to groom child workers.

You will be in the orphanage system until you about 16 years old, in which case you're either transferred to another facility that deal with adults (like and institution) or, if you're lucky enough to be able to fend for yourself, you can go out on your own.

My original post did not meet the guidelines so Ill try again because this is such an overlooked subject.

It would largely depend on your age when you were abandoned. In London you would likely be taken in by the Children' Friend Society but there were many such organizations throughout England and Scotland. Annie MacPhearson and Dr Bernardo's home for waifs and strays were two of the larger ones. Girls were trained in domestics and boys learned farming and they were then sent to Canada, Australia and New Zealand. Often the children were told that their parents were dead or did not want them anymore and they were given promises of a better life in their new country. Over 100 thousand Home Children were sent to Canada alone.

Once in Canada, conditions varied depending on the family that took you in. Some were lucky and had their Oliver Twist happy ending but most were treated very harshly and many ended up running away.