I would forego the using of titles when writing a review like this. One can create a similar layout without using any titles and it provides you more freedom in terms of the layout:

\documentclass{article}
\usepackage{titling,lipsum}% http://ctan.org/pkg/{titling,lipsum}
\pretitle{\begin{flushleft}\LARGE\textbf}
\posttitle{\vskip .25ex\hrule\par\end{flushleft}}
\preauthor{\begin{flushleft}\large}
\postauthor{\par\end{flushleft}}
\predate{\begin{flushleft}}
\postdate{\par\end{flushleft}}
\begin{document}
%%%% Old definition of Review
\title{Review}
% The bibliographic details about the book I'm reviewing go between the title and my author details.
\author{\textbf{Paul McCartney}\\ University of Liverpool}
\date{\today}
\maketitle
\noindent Here my review begins
\clearpage
%%%% New definition of Review
\raggedright
\textbf{\LARGE Review}
\hrulefill
\medskip\par
\lipsum[1]
\bigskip
{\large\textbf{Paul McCartney}\par
University of Liverpool\par}
\medskip
\today
\bigskip
Here my review begins
\end{document}
A separate structure/content approach would include something like this:

\documentclass{article}
\usepackage{lipsum}% http://ctan.org/pkg/lipsum
\makeatletter
\newcommand{\reviewtitle}[1]{\def\@reviewtitle{#1}}
\newcommand{\reviewtitleformat}[1]{\def\@reviewtitleformat{#1}}
\newcommand{\bookauthor}[1]{\def\@bookauthor{#1}}
\newcommand{\bookauthorformat}[1]{\def\@bookauthorformat{#1}}
\newcommand{\booktitle}[1]{\def\@booktitle{#1}}
\newcommand{\booktitleformat}[1]{\def\@booktitleformat{#1}}
\newcommand{\reviewauthor}[1]{\def\@reviewauthor{#1}}
\newcommand{\reviewauthorformat}[1]{\def\@reviewauthorformat{#1}}
\newcommand{\reviewauthorsub}[1]{\def\@reviewauthorsub{#1}}
\newcommand{\reviewauthorsubformat}[1]{\def\@reviewauthorsubformat{#1}}
\newcommand{\reviewdate}[1]{\def\@reviewdate{#1}}
\newcommand{\reviewdateformat}[1]{\def\@reviewdateformat{#1}}
\renewcommand{\maketitle}{%
{\@reviewtitleformat\@reviewtitle}
\hrulefill
\medskip\par
{\@booktitleformat\@booktitle\par}
{\@bookauthorformat\@bookauthor\par}
\bigskip
{\@reviewauthorformat\@reviewauthor\par}
{\@reviewauthorsubformat\@reviewauthorsub\par}
\medskip
{\@reviewdateformat\@reviewdate\par}
\bigskip
}
\makeatother
\reviewtitle{Review}
\reviewtitleformat{\bfseries\LARGE}
\reviewauthor{Paul McCartney}
\reviewauthorformat{\bfseries\large}
\reviewauthorsub{University of Liverpool}
\reviewauthorsubformat{\large}
\booktitle{Book title \\ \lipsum[2]}
\booktitleformat{\itshape}
\bookauthor{Some Author}
\bookauthorformat{\bfseries}
\reviewdate{\today}
\reviewdateformat{\normalfont}
\begin{document}
\raggedright
\maketitle
Here my review begins
\end{document}