In the absence of other software, just open up the gpx file in Notepad or whatever, and delete the lines between the last trackpoint in the first active log and the first trackpoint in the second active log.
(as highlighted in red below)
...
<trkpt lat="51.861718" lon="-2.223100">
<ele>-78.207</ele>
<time>2011-05-10T16:24:13Z</time>
</trkpt>
</trkseg>
</trk>
<trk>
<name>ACTIVE LOG172431</name>
<trkseg>
<trkpt lat="51.861718" lon="-2.223100">
<ele>-77.964</ele>
<time>2011-05-10T16:24:31Z</time>
</trkpt>
...