What will happen to the convict if he is found in London?

The basic answer to this is that he will be sentenced to
death if he is found and identified in London or anywhere else in
Britain.

The reason for this is found in his original
sentence.  He was sentenced to be "transported."  This meant that he was sent to
Australia instead of being executed or imprisoned in Britain.  But the other side of
that deal is that he was never allowed to return to
Britain.

Now that he has returned, he is risking death. 
You will find out later in the book whether he will get caught and face death or
not.