Surface Electromyography (sEMG) is widely studied for its applications in rehabilitation, prosthetics, robotic arm control, and human-machine interaction. However, classifying Activities of Daily Living (ADL) using sEMG signals often requires extensive feature extraction, which can be time-consuming and energy-intensive. The objective of this study is stated as follows. Given sEMG datasets, such as electromyography analysis of human activity databases (DB1 and DB4), with multi-channel signals corresponding to ADL, is it possible to determine the ADL categories without explicit feature extraction from sEMG signals. Further is it possible to learn across the datasets to improve the classification performances. A classification framework, named EMGTTL, is developed that uses transformers for classification of ADL and the performance is enhanced by cross-data transfer learning. The methodology is implemented on EMAHA-DB1 and EMAHA-DB4. Experiments have shown that the transformer architecture achieved 64.47% accuracy for DB1 and 68.82% for DB4. Further, using transfer learning, the accuracy improved to 66.75% for DB1 (pre-trained on DB4) and 71.04% for DB4 (pre-trained on DB1).