How to isolate GPS tracks, which I have in .gpx format, for a specific area only?

If you do not need the original file name of the gpx and also do not need the original time stamps, but just the relevant trace itself, then you could use the OSM-Editor JOSM for this:

1. open JOSM
2. step 11 needs "expert mode", so activate it. It may be a good idea to disable it afterwards (unless you like to continue to use JOSM's expert interface).
3. load all gpx files
4. in the layers dialog: select all layers
5. rightclick on of the gpx entries in the layers dialog, select "merge"
6. rightclick the resulting layer, select "convert to data layer"
7. in the editing map zoom to the location you are interested in and just click one of the tracks (btw: now it is a OSM way) to select it
8. copy (ctrl+C) the track
9. create a new layer
10. paste the copied track (ctrl+V)
11. export the data layer into a gpx file

note: Please do not "upload" such converted gpx tracks to OSM with JOSM's normal upload feature! Best: restart JOSM before you continue with your normal OSM contributions/editing.

Some of the tools listed there https://wiki.openstreetmap.org/wiki/Edit_GPS_tracks may help

I would turn to OSGeo tools for this.

A very quick check shows that ogrinfo will provide information about a wide range of files containing geographic information, including GPX. Part of this information is extents of the file, or layer. So post-processing gdalinfo output (as simple as grepping for "Extents" could provide you a listing of the extents for each gpx file.

Once you have the information it may be useful to store it in a spatial database to easily relocated relevant GPX files.

Echoing the SK53 answer "I would turn to OSGeo tools for this", but instead of ogrinfo, use ogr2ogr to convert your GPX traces into a shape file (possibly running ogr2ogr multiple times with the same output file, using -append from the second run on), and then again use ogr2ogr with the -spat option and a London bounding box to select those traces that go through London. Then you can use QGIS to visualize them if desired.

In pseudo code:

ogr2ogr trails.shp track1.gpx
ogr2ogr -append trails.shp track2.gpx 
...
ogr2ogr -append trails.shp track999.gpx
ogr2ogr -spat -0.4 51.3 0.3 51.7 london-trails.shp trails.shp
qgis london-trails.shp

There's any number of potential traps here, e.g. how to keep attributes of your GPX file if you need them, or what happens if one GPX contains multiple tracks, or whether you want to process routes or tracks, etc., but with some patience and the right command line flags, things should turn out nicely.

The advantage of this more complex process is that it will actually look at the track, not only the bounding box. (Even though it will only allow a rectangular "London".)

Lastly, if you want to go super analytic on this, you could also import your shape file into a PostGIS database which would then allow you to check against a polygonal London boundary, or run queries like "which trails are in London for more than 50% of their length", "which trails are in London for more than 2km", or "which trails start in London and end more than 20km away" and whatnot.

And no, this question is not OpenStreetMap related and should have been asked elsewhere.

This shows a picture of GPS prune with hundreds of footpath kml files of several counties, it will also display mutiple GPXes. Multiple traces can be added with ctrl select. If you zoom in and click on a trace it will tell you the trace's id and other info all displayed on over OSM. The kml are from http://www.rowmaps.com/ and prune is from here http://activityworkshop.net/software/gpsprune/ Prune may help you. and if you have an interest England's Rights of Way the other link is very useful.