All conveyancers must be a member of the Law Society (if they are also a solicitor) or of the Council of Licensed Conveyancers (CLC). Complaints about solicitors are handled by the Legal Complaints Service and complaints about Licensed Conveyancers by the CLC.
You should complain to your conveyancer and give them a fair chance to sort out the problem before approaching either body.
If you are not satisfied with the outcome of an internal complaint, contact the relevant organisation.