The answer depends on the ownership and management structure of your block. Most residential blocks of flats operate under a tri-party lease arrangement involving a freeholder, a management company (usually an RMC or RTM company), and the individual leaseholders.
If your block has a Resident Management Company (RMC) or a Right to Manage (RTM) company, the directors of that company typically have the authority to appoint and remove the managing agent. This means the board can vote to terminate the existing management agreement and appoint a replacement, subject to the terms of the contract (usually a notice period of one to three months).
If your block does not have an RMC and the managing agent was appointed directly by the freeholder, the situation is different. In this case, leaseholders may need to exercise their Right to Manage under the Commonhold and Leasehold Reform Act 2002 to take control of the appointment process.
If the managing agent is named directly in your lease, you may still be able to change them. Seek legal advice, as the process may involve a variation of the lease or an application to the First-tier Tribunal (Property Chamber).