Please try the following changed code:
\documentclass{article}
\usepackage{graphicx} %to import images
\usepackage{float} %control of float positions
\usepackage{fancyhdr}
\pagestyle{fancy}
\begin{document}
\begin{titlepage}
\begin{center}
\huge{\bfseries The Collisionless Dynamics of the Milky Way}\\
[12cm]
\end{center}
\begin{flushright}\
\textsc{\large name}
\\130009548\\
\end{flushright}
\end{titlepage}
% table of contents stuff
\tableofcontents
\thispagestyle{empty}
\cleardoublepage
\setcounter{page}{1}
\section{Introduction}\label{sec:intro}
Some text for my intro
\begin{figure}[H]
\centering
\includegraphics[height=3in]{//cfs/users/sm292/Documents/Pictures/MWmodella.jpg} % <=================
\caption{Structure of the Milky Way} % <==============================
\end{figure} % <================================================ missing
\end{document}
Please see that I changed the lines marked with <=======. Please see that I added the missing \end{figure}.
Please see that I corrected the line: \caption{Structure of the Milky Way}. The figure numbering is done by LaTeX ...
Because I do not have the called file MWmodella.jpg I get the following result:

Because I do not have your image I use the package MWE (must be installed, but not called) to show the result with example-image-a: \includegraphics[height=3in]{example-image-a}.
With the MWE
\documentclass{article}
\usepackage{graphicx} %to import images
\usepackage{float} %control of float positions
\usepackage{fancyhdr}
\pagestyle{fancy}
\begin{document}
\begin{titlepage}
\begin{center}
\huge{\bfseries The Collisionless Dynamics of the Milky Way}\\
[12cm]
\end{center}
\begin{flushright}\
\textsc{\large name}
\\130009548\\
\end{flushright}
\end{titlepage}
% table of contents stuff
\tableofcontents
\thispagestyle{empty}
\cleardoublepage
\setcounter{page}{1}
\section{Introduction}\label{sec:intro}
Some text for my intro
\begin{figure}[H]
\centering
\includegraphics[height=3in]{example-image-a} % <=================
\caption{Structure of the Milky Way} % <==============================
\end{figure} % <================================================ missing
\end{document}
you get the result:
