Generally a lawyer owes a client a duty of both confidentiality and loyalty. However, a lawyer also has a right to transfer to another law firm, assuming that appropriate measures are taken to ensure that the lawyer's duties of confidentiality and loyalty are preserved. A recent case that Terry Robertson, Q.C. and myself argued, Slater Vecchio v. Robertson et al., explored the ability of a lawyer to move from a firm that performed work for an insurer, to a personal injury firm, that commonly represented clients against that same insurer. One fact that complicated the issue was that the lawyer that transferred to the new law firm was representing a client and his insurer, that were sued by a client represented by the law firm that he moved to. The lawsuit was ongoing at the time of the transfer. There was no consent from the former clients. The law firms where small and the transfered lawyer was, likely, in daily contact, with the lawyer and staff who were prosecuting the action against the transfered lawyer's former clients.
The matter is currently under appeal to the British Columbia Court of Appeal. Here is a link to the reasons granting leave to appeal, and here is a link to reasons from the British Columbia Court of Appeal deciding that an appeal from a judge's decision to enjoin a law firm from acting on a file due to a conflict of interest is a matter of practice and requires leave.
Sarah Swan and Sandra Kovacs wrote an article on this issue.
Here is a copy of the article.