Three of the SP MLCs who had resigned have already joined the BJP and Mr Bajpai is also expected to follow suit, sources said.
"I am tendering my resignation from the Council membership. I am peeved at the treatment meted to 'Netaji' (Mulayam Singh Yadav) in the party," Mr Bajpai told reporters after giving his resignation to Council Chairman Ramesh Yadav.
On August 4, SP MLC Sarojini Agarwal resigned from the Legislative Council membership and joined the BJP.
On the reasons of her resignation, she had said she was not feeling comfortable in the party as Mulayam was not given any importance.
"I had been party MLC twice due to netaji. As he is not active in the party, I have resigned. I don't have problems with anyone in the party and I respect everyone. I felt awkward after split in the party and I did not feel like working in it," Ms Agarwal had said.
Earlier on July 29 during BJP President Amit Shah's visit to the state capital, two SP and one BSP MLCs had resigned and joined BJP.
The resignation of five MLCs including (four of the SP and one BSP) assumes significance as BJP has to soon take a decision on five of its ministers in Uttar Pradesh, including Chief Minister Yogi Adityanath, who are not members of either of the two Houses.
Besides Yogi Adityanath, Deputy Chief Ministers Keshav Prasad Maurya and Dinesh Sharma, ministers Swatantra Dev Singh and Mohsin Raza are not members of either of the two Houses.
They have to be elected to either of the Houses in order to continue as ministers.
With the resignations in Council, the entry of these leaders in the House is considered to be an easy task.
Get the latest election news, live updates and election schedule for Lok Sabha Elections 2019 on ndtv.com/elections. Like us on Facebook or follow us on Twitter and Instagram for updates from each of the 543 parliamentary seats for the 2019 Indian general elections. Election results will be out on May 23.