These are both forms of intermolecular forces (attractions BETWEEN the molecules)
Intermolecular forces are weaker than the INTRAmolecular forces that hold the atoms within a molecule together. They explain why the molecules are held together in a liquid or solid rather than floating around solo!
London forces are the weakest of this intra type – within a molecule there are temporary fluctuations in the polarity because of the random and unbalanced movement of electrons about its nucleus. These imbalances give an unsymmetrical shape of electron distribution and so the instantaneous dipole momentarily attracts its neighbour who also has a momentary unsymmetrical distribution.
Because these electron distributions are fleeting, the dipole is instantaneous – that is, it hardly lasts long enough to form any sort of formal attraction. Overall though a molecule will have an attraction to any one (or more) of its neighbours.
Dipole-dipole attractions are a little more permanent, and are stronger than the London forces. This is where there is a permanent unsymmetrical distribution of electrons, typically because the atom is electronegative and so pulls the electrons towards itself within the molecule. Because the electrons are going to be found around that atom more often, that area of the molecule will be more negatively charged meaning that there is a more positively charged end within the same molecule.
And since that is happening to all the molecules within the solution, one molecules negatively charged dipole will be attracted to another molecules positively charged dipole.
And so… you can see how London forces are a general force that happens to all solutions, whereas dipole-dipole forces would only ever happen when the molecules in question have a permanent dipole. The strength of the dipole-dipole force would then depend on the polarity of the molecule (more electrons/ high electronegativity = greater difference in dipole = greater force strength)!