The role of natural factors mainly solar eleven-year cycle variability, and volcanic eruptions on two major modes of climate variability the North Atlantic Oscillation (NAO) and El Niño Southern Oscillation (ENSO) are studied for around last 150 years period. The NAO is the primary factor to regulate Central England Temperature (CET) during winter throughout the period, though NAO is impacted differently by other factors in various time periods. Solar variability indicates a strong positive influence on NAO during 1978-1997, though suggests opposite in earlier period. Solar NAO lag relationship is also shown sensitive to the chosen times of reference and thus points towards the previously proposed mechanism/ relationship related to the sun and NAO. The ENSO is influenced strongly by solar variability and volcanic eruptions in certain periods. This study observes a strong negative association between the sun and ENSO before the 1950s, which is even opposite during the second half of 20th century. The period 1978-1997, when two strong eruptions coincided with active years of strong solar cycles, the ENSO, and volcano suggested a stronger association, and we discussed the important role played by ENSO. That period showed warming in central tropical Pacific while cooling in the North Atlantic with reference to the later period (1999-2017) and also from chosen earlier period. Here we show that the mean atmospheric state is important for understanding the connection between solar variability, the NAO and ENSO and associated mechanism. It presents a critical analysis to improve knowledge about major modes of variability and their role in climate. We also discussed the importance of detecting the robust signal of natural variability, mainly the sun.