It's a while since I've been. Was always something of an adventure - former railway embankment with bridge over Newcraighall Road. Used to be 'dangerous' due to underground fires - think they have been bulldozed out of existance. Land is/was owned by Sustrans.
(from Is it really safer to wear a helmet?)
I had a look today. Well actually I had a look at the great big locked gate at the southern end of the old embankment, which comes out in what is now the car park of Musselburgh Station. No access from there.
I cast an eye over the possible entrance off Newcraighall Road but it looked to be private. Of course, the footbridge in chdot's picture is more or less on the join between the Edinburgh and East Lothian Spokes maps, and as I cycled around QMU towards Millerhill, I had forgotten that the bridge was further west along Newcraighall Road. Annoyingly, I would have found it quite easily if I'd taken the right-hand fork on the old railway path from Brunstane/Gilberstoun Loan to N'hall Rd.
I'll just have to visit the area again, probably once the sun is actually shining.