This paper presents measurements of K-0 and Lambda production in neutral current, deep inelastic scattering of 26.7 GeV electrons and 820 GeV protons in the kinematic range 10 0.04. Average multiplicities for K-0 and Lambda production are determined for transverse momenta p(T) > 0.5 GeV and pseudorapidities \eta\ < 1.3. The multiplicities favour a stronger strange to light quark suppression in the fragmentation chain than found in e(+)e(-) experiments. The production properties of K-0's in events with and without a large rapidity gap with respect to the proton direction are compared. The ratio of neutral K-0's to charged particles per event in the measured kinematic range is, within the present statistics, the same in both samples
