Laser-plasma accelerators can produce ultra-short electron bunches in the femtosecond to picosecond duration range, resulting in very high peak dose rates in comparison with clinical accelerators. This unique characteristic motivates their possible application to radiation biology studies to elucidate the effect of high peak dose rates and peculiar temporal structures on the biological response of living cells, which might improve the differential response between tumour and healthy tissues. Electron beams driven by kHz laser systems are an attractive option among laser-plasma accelerators since the high repetition rate can boost the mean dose rate and improve the stability of the delivered dose in comparison with J-class laser accelerators running at few Hz. In this work, we present the dosimetric characterisation of a kHz, low energy laser-driven electron source and preliminary results on in-vitro irradiation of cancer cells. A shot-to-shot dosimetry protocol enabled monitoring of the beam stability and the irradiation conditions for each cell sample. Results of survival assays on HCT116 colorectal cancer cells are in good agreement with previous findings reported in the literature and validate the robustness of the dosimetry and irradiation protocol.