How to (manually) set the date in a letter?

Just add \date{} somewhere before \begin{opening}. For instance, in your document:

\documentclass{letter}
\usepackage{hyperref}
\signature{Joe Bloggs}
\address{21 Bridge Street \\ Smallville \\ Dunwich DU3 4WE}
\begin{document}

\begin{letter}{Director \\ Doe \& Co \\ 35 Anthony Road
\\ Newport \\ Ipswich IP3 5RT}
\date{October 21, 2014}
\opening{Dear Sir or Madam:}
...