XSLT Transform doesn't work until I remove root node
The problem: your XML puts its elements in a namespace.
Solution: declare the same namespace in your stylesheet, assign it a prefix and use that prefix to address the elements in the source XML:
XSLT 1.0
<xsl:stylesheet version="1.0"
xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
xmlns:met="www.metoffice.gov.uk/xml/metoRegionalFcst"
exclude-result-prefixes="met">
<xsl:template match="/">
<html>
<body>
<xsl:value-of select="met:RegionalFcst/met:FcstPeriods/met:Period/met:Paragraph[@title='Headline:']"/>
</body>
</html>
</xsl:template>
</xsl:stylesheet>