natbib needs the author and year information in the optional argument of \bibitem to be in a special format so it can be parsed. natbib.sty explains the possible formats in a comment
% If author-year citations are selected, \bibitem must have one of the
% following forms:
% \bibitem[Jones et al.(1990)]{key}...
% \bibitem[Jones et al.(1990)Jones, Baker, and Williams]{key}...
% \bibitem[Jones et al., 1990]{key}...
% \bibitem[\protect\citeauthoryear{Jones, Baker, and Williams}{Jones
% et al.}{1990}]{key}...
% \bibitem[\protect\citeauthoryear{Jones et al.}{1990}]{key}...
% \bibitem[\protect\astroncite{Jones et al.}{1990}]{key}...
% \bibitem[\protect\citename{Jones et al., }1990]{key}...
% \harvarditem[Jones et al.]{Jones, Baker, and Williams}{1990}{key}...
The format used in the question
\bibitem[(Charles, 1985)]{Charles85}
is not among the supported formats. The simplest way to make the information digestible for natbib is probably by dropping the parentheses to make it read
\bibitem[Charles, 1985]{Charles85}
Alternatively, you could use the format that natbib's standard .bst files use
\bibitem[Charles(1985)]{Charles85}
In total
\documentclass[british]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{babel}
\usepackage{natbib}
\begin{document}
\citep{Charles85,Smith89}
\begin{thebibliography}{99}
\bibitem[Charles, 1985]{Charles85} Anne Charles: \emph{Title}. 1985
\bibitem[Smith, 1989]{Smith89} Jane Smith: \emph{Another Title}. 1989
\end{thebibliography}
\end{document}

That said, it is usually more comfortable to use .bib files and BibTeX (or biblatex and Biber: bibtex vs. biber and biblatex vs. natbib) instead of a manual thebibliography. Entries can be re-used and re-styled more easily and BibTeX (or Biber) takes care of sorting.
(<Name>, <Year>)is not a formatnatbibcan parse in the optional argument to\bibitem. Drop the parentheses and try<Name>, <Year>:\bibitem[Charles, 1985]{Charles85}– moewe Mar 12 '19 at 21:41