In many countries, individuals are allowed to freely choose their provider of publicly funded services such as schooling or healthcare services. Judging the quality of such credence goods may be challenging, and the ability to identify high-quality providers presumably follows a socioeconomic gradient. This study explores socioeconomic disparities in how patients trade off quality against other features when choosing their primary care provider. We use a unique registry dataset linking the choices of individuals who recently moved to a new market, and therefore need to select a new provider, with detailed individual-level measures of socioeconomic status (SES) and provider-level measures of patient satisfaction, clinical quality and travel distance in a large Swedish region. We find significant disparities in patient choice based on SES, as high-SES individuals are consistently more likely to select higher quality providers. However, the results also suggest that most of the SES disparities in observed quality are linked to differences in the availability of high-quality providers within an acceptable travel distance. Our findings suggest that patient choice can widen, rather than reduce, disparities in population health by SES -- if spatial inequalities in access to high-quality care are not addressed beforehand.