Given the current pandemic, there has been much attention in the analysis of chest Computed Tomography (CT) scan images using deep learning architectures for the detection of COVID-19 in a clinical setting. The success of deep learning models is highly dependent on large reliable datasets, however in medical imaging paucity of data is a well-known problem. To address this issue, here we propose Indian-COVID-19 CT dataset, which is a collection of chest CT images of COVID-19 patients from India. Currently it consists of 12,096 images from 288 COVID-19 patients, obtained from a single hospital with same image acquisition clinical settings. To the best of our knowledge, this is the only dataset available from Indian population making it a valuable addition to other similar COVID CT image repositories. It has been built and curated to aid in the diagnosis of COVID-19 and other chest CT analysis tasks using machine learning algorithms such as developing generalizable and robust models for various lung disease detection tasks. In this paper we also propose a lightweight Convolutional Neural Network (CNN) model for the diagnosis of COVID-19 to address the problem of faster diagnosis and patient prioritization. The simple architecture and small number of parameters makes the proposed model suitable for a clinical setting. The model has been trained and validated on publicly available dataset, COVIDx-CT, to classify chest CT scans into three classes, viz., Normal, non-Covid Pneumonia and COVID-19. Performance of the model is evaluated on both COVIDx-CT and Indian-COVID-19 CT datasets. The efficacy of the simple CNN model in classifying CT images is also shown to be comparable to four state-of-the-art deep learning models, viz., VGG-16, ResNet50, InceptionNetV3 and EfficientNetB7.