To what extent do contemporary web technologies that seek to personalize users' browsing experience trap them in filter bubbles? Existing research has yielded mixed results on the possibility of such influence, but empirical research in this area has been entirely cross-sectional. In this paper, we report results from a longitudinal controlled web experiment conducted to determine whether passive recommendations embedded in common computer user-interfaces (UIs) reinforce users' habitual browsing behaviors, to the detriment of the diversity of the set of pages they tend to visit online. Inspired by classical demonstrations of a part-set cueing effect in memory, our experimental design manipulates the behaviour of the 'New Tab' page for consenting volunteers over a two month-long period in randomized time blocks of equal length. Analysis of their browsing behavior shows that users visit on average 15% fewer unique web pages while their browser's 'New Tab' page displays recommendations based on conventional frequency and recency-based algorithms, than if the display is left blank. This effect is seen systematically for all participants in our study. Further analysis of browsing behavior in this experiment clearly identifies the source of the difference between these modes of browsing: users consistently visit a greater diversity of web pages while typing in URLs in the URL/search bar when there are no recommendations on the 'New Tab' page. Finally, using a simulation study, modelling user behavior as a random walk on a graph, we extracted quantitative predictions about the extent to which discovery of new sources of information may be hindered by the concentration of browsing driven by such personalized 'New Tab' recommendations in classical browser UIs.