The road is expected to be closed until Monday
Investigators and forensics teams are at the cordoned off scene near the A404 at High Wycombe, following the discovery on Saturday at 1.40pm.
Thames Valley Police have confirmed the remains are human but would not give any further details. The force said the death is being treated as unexplained.
The slip road that feeds on to the M40 northbound at junction 4 is expected to stay closed until Monday.