In this paper, the one-dimensional (1D) time-dependent behaviour of natural and reconstituted London Clay samples under saturated and unsaturated conditions is studied. For this purpose, a set of 1D consolidation tests including multi-staged loading (MSL) oedometer tests and single-staged loading (SSL) long-term oedometer creep tests were carried out on saturated and unsaturated specimens. Conventional oedometer cells were used for tests on saturated specimens, whereas a newly designed unsaturated oedometer cell, equipped with two high-capacity tensiometers (HCTs) for suction measurements, was used for unsaturated tests. The tests results revealed stress dependency and suction dependency of primary and secondary consolidation responses of the soil samples. Furthermore, counter to formerly acknowledged suggestions of independency of the slope of normal consolidation line to suction changes, it was observed that an increase in suction results in a decrease of the slope of compression curve (Cc) and the creep index (Cαe) values and an increase in yield vertical net stress (σp). Moreover, the Cαe/Ccratio for London Clay was found to be stress- and suction-dependent, unlike the previously suggested hypotheses.