A good few years ago someone came up with a journey (using British/National Rail only) requiring 7 changes , but service changes have now reduced it to 3.
If I recall correctly, it was from Southminster branch to one particular station on the Sheerness branch (Swale Halt or Kemsley - whichever did not have a through train from London). Changing at Wickford (nothing through off the branch than), Stratford (this was long before HS1), Highbury & I (no through NLL trains then), Willesden Junction (or possibly it was Richmond, pre WLL), Clapham Junction, Victoria (?) and Sittingbourne.