A theory of the coagulation rate in concentrated suspensions of Brownian particles, interacting via the familiar Derjaguin - Landau - Verwey - Overbeek (DLVO) pair potential, is proposed. An effective pair potential between two coagulating particles is obtained by thermally averaging over the fluctuating cage of neighbouring particles and thereby the problem can be treated within a modified Smoluchowski - Debye approach. Testing the theory against extensive Brownian dynamics computer simulations, reasonable agreement is found.