This work studies 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) 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 different time periods. Solar variability has a positive influence on NAO during 1978-1997, which is opposite before that period. Solar NAO lag relationship is also sensitive to the chosen times of reference. Such analyses raise a question about previously proposed mechanism and relationship related to the sun and NAO. The ENSO is seen to be influenced strongly by solar variability and volcanic eruptions in certain periods. This study observes a strong negative association between solar variability 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 volcanic eruptions suggested the stronger association. Here we show that the mean atmospheric state is important for understanding the connection between solar variability, the NAO and ENSO and associated mechanism.