Dave,
There are a number of main routes that REACH aircraft take when transiting across the UK.
Eastbound from the SW; GITUS>DIKAS>MAM and then NAVPI if not landing at EGUN. They reverse the route going West.
Eastbound coming in from the NW e.g;
GOMUP/GINGA/MIMKU>HERON>BAGPO>TIPTA>DOLAS>NALAX>NAVPI.
Eastbound from the West;
REMSI>POL>GOLES>OTBED>DOLAS>NAVPI
Although these are the most common routes they can vary depending on wx, range and other traffic.
If you are really interested in REACH aircraft tracking you should join a group such as Reach Hunters International at
http://groups.yahoo.com/You could also consider purchasing PlanePlotter by COAA which will allow you access to their free network and which, with their low cost multilateration option, will allow you to track most non-positional aircraft.
Tom