Get the tube from LHR to Hatton Cross. Then walk to The Rivers. Look on Google Maps (put Hatton Cross in the search). Look for the Eastern Perimeter Road, (which goes past the Jurys Inn and staff car parks) and walk to the mini roundabout which is opposite the end of the car parks. You'll then see a barrier across the road to stop cars (2nd exit on the mini rb), but you can walk past it and onto The Rivers (the little security hut where you sign in is about 100m or so on the left after the security barrier, which I think is called Kenny's Gate, but I could have got the name wrong.) No more than 10-15 mins walking from Hatton Cross.
Alternate options are the Hotel Hoppa bus to the Jurys Inn, then walk, but the Hotel Hoppas are not that frequent, or the BA1 staff bus (which your paper work will get you on), I don't know where in T5 that goes from, but it does go from Hatton Cross to Cranebank.
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