Below is a current low altitude airway (24,500ft and below) Map os the SE
And this one is a high altitude airways (24,500ft and above)
Rough arrival routes are below:
Arrivals into LHR
from the North route in via WCO and BNN (BNN not on the map, but is approximatly where airways H52 and L186 on the low alt airway chart cross) From the east the route in via LAM. South east arrivals arrive in via BIG, Southwest arrivals arrive in via OCK. Arrivals via OCK, arrive via NUMPO and HAZEL before reaching OCK.
Gatwick arrivals route from the north via KIDLI and MID
before heading towards MAY. Arrivals from the east route from KOPUL to TANET onwards to DET before heading towards LYD, before turning back towards MAY.
South east arrivals arrive via airway UM733 / M733 before heading towards MAY, south west arrivals arrive via GWC, before going agaun, towards MAY.
Hope this helps.