\documentclass{letter}
\usepackage{graphicx}
\usepackage[top=0.1in]{geometry}
\usepackage{tikz}
\usepackage{tikzpagenodes}

\signature{\vspace{-1.5cm}NAME HERE}
\address{\vspace{2cm} \\ Computer \& Information Sciences \\ University of Strathclyde \\ Livingstone Tower \\ 26 Richmond Street \\ Glasgow \\ G1 1XH}
\date{DATE}

\begin{document}

\begin{letter}{}

\begin{tikzpicture}[remember picture,overlay,shift={(current page.north east)}]
  \node[anchor=north east,xshift=-3cm,yshift=0.2cm]{\includegraphics[width=4cm]{strath_tab_sci.pdf}};
\end{tikzpicture}
\begin{tikzpicture}[remember picture,overlay,shift={(current page.south west)}]
  \node[anchor=south west,xshift=3cm,yshift=1cm]{\footnotesize{The University of Strathclyde is a charitable body, registered in Scotland, number SC015263.}};
\end{tikzpicture}


\opening{Dear X,}


\closing{Yours sincerely, }% \\\vspace{1cm} \includegraphics[width=2cm]{signature.jpg}}



\end{letter}


\end{document}