It would be much easier if you could use XSLT 2.0 or higher. It could be as simple as:
replace(replace(., '\$key1\$', 'London'), '\$key2\$', 'England')
However, if you are stuck with XSLT 1.0, you could use a recursive template to perform the replace, and invoke it for each of the tokens you want to replace(using the product of the previous calls as input to the next):
<?xml version="1.0" encoding="UTF-8"?>
<xsl:stylesheet xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
xmlns:client="http://xmlns.oracle.com/ErrorHandler"
version="1.0">
<xsl:template name="replace-string">
<xsl:param name="text"/>
<xsl:param name="replace"/>
<xsl:param name="with"/>
<xsl:choose>
<xsl:when test="contains($text,$replace)">
<xsl:value-of select="substring-before($text,$replace)"/>
<xsl:value-of select="$with"/>
<xsl:call-template name="replace-string">
<xsl:with-param name="text"
select="substring-after($text,$replace)"/>
<xsl:with-param name="replace" select="$replace"/>
<xsl:with-param name="with" select="$with"/>
</xsl:call-template>
</xsl:when>
<xsl:otherwise>
<xsl:value-of select="$text"/>
</xsl:otherwise>
</xsl:choose>
</xsl:template>
<xsl:template match="@*|node()">
<xsl:copy>
<xsl:apply-templates select="@*|node()"/>
</xsl:copy>
</xsl:template>
<xsl:template match="client:result">
<xsl:variable name="orig" select="string(.)"/>
<xsl:variable name="key1">
<xsl:call-template name="replace-string">
<xsl:with-param name="text" select="$orig"/>
<xsl:with-param name="replace" select="'$key1$'"/>
<xsl:with-param name="with" select="'London'"/>
</xsl:call-template>
</xsl:variable>
<xsl:variable name="key2">
<xsl:call-template name="replace-string">
<xsl:with-param name="text" select="$key1"/>
<xsl:with-param name="replace" select="'$key2$'"/>
<xsl:with-param name="with" select="'England'"/>
</xsl:call-template>
</xsl:variable>
<xsl:copy>
<xsl:value-of select="$key2"/>
</xsl:copy>
</xsl:template>
</xsl:stylesheet>