Is there a relationship between London dispersion forces and hydrophobic interactions?
To summarize the excellent but rather lengthy and detailed Stack Exchange answer referred to by Andy above, hydrophobic interactions do not require London forces between the hydrocarbon chains. They are a result of the very strong attraction of water for itself. 

I would further quote the following comment to that entry (by https://chemistry.stackexchange.com/users/5633/thomij), which I think sums it up nicely:

"This is a good answer, but the last part about van-der waals forces being required to pull the hydrophobic solvent together is incorrect. If you had particles with no attractive forces between them in a solvent that has attractive forces, as long as the enthalpy drop for phase separation is larger than the entropic penalty, they will separate. Van der waals forces help to make the enthalpy drop larger, but they aren't necessary. –  thomij Jun 23 '14 at 19:02"