Bibtex “didn't find a database entry”

Your file Quotes.bib should look like this:

@Article{Haggarty:01,
  author =   {Haggarty, L. and Pepin, B.},
  title =    {An Investigation of Mathematics Textbooks and their
                  use in English, French and German Classrooms},
  journal =  {Proceedings of the British Society for Research into
                  Learning Mathematics},
  year =     2001,
  volume =   21,
  number =   2,
  pages =    {117--125}
}

Compiling your main file with latex, bibtex, latex, latex gives:

What you have used instead is something akin to the .bbl file that is the result of running latexfollowed by bibtex. Once you have a final list of references such a .bbl file could be included directly in to your main source to make a standand alone document of the form:

\documentclass[11pt]{article}

\usepackage[round]{natbib}

\begin{document}

Their long-term aid \citet{Haggarty:01}

%\bibliographystyle{plainnat}
%\bibliography{Quotes}
\begin{thebibliography}{1}
\providecommand{\natexlab}[1]{#1}
\providecommand{\url}[1]{\texttt{#1}}
\expandafter\ifx\csname urlstyle\endcsname\relax
  \providecommand{\doi}[1]{doi: #1}\else
  \providecommand{\doi}{doi: \begingroup \urlstyle{rm}\Url}\fi

\bibitem[Haggarty and Pepin(2001)]{Haggarty:01}
L.~Haggarty and B.~Pepin.
\newblock An investigation of mathematics textbooks and their use in english,
  french and german classrooms.
\newblock \emph{Proceedings of the British Society for Research into Learning
  Mathematics}, 21\penalty0 (2):\penalty0 117--125, 2001.

\end{thebibliography}

\end{document}