Prof. Robert Flannigan just published an insightful piece on UK disqualification practice.  Perhaps unsurprisingly, solicitors face disqualification most commonly in situations in which they either represent a current client adversely to another current client or represent a current client against a former client in an arguably related matter.  (Likewise, these are the two most common categories in the United States.)  The abstract of, and link to, the article follow:

Solicitors regularly must assess whether to decline or end retainers because of possible conflicts with the interests of current or former clients. If they proceed with a questionable retainer, a current or former client may object, and a judge may order that they be restrained from acting. The jurisprudence that has developed on the judicial power to restrain or disqualify solicitors obviously is a key source of guidance for those who must confront the issue. Unfortunately the jurisprudence is uncertain. An initial difficulty is the failure to identify credibly the policy considerations that are relevant. A second difficulty is that, as the following analysis will show, the precise nature of the test for disqualification has remained elusive. A significant weakness with the judicial analysis is its focus on negligence by solicitors, rather than opportunistic conduct by them. Correcting that analytical deficiency is necessary to nurture both the fact and appearance of high professional conduct.

Robert Flannigan, Judicial Disqualification of Solicitors with Client Conflicts, 130 Law Quarterly Review 498 (2014).