Plant-based food alternatives have increased in popularity, particularly plant-based meat alternatives, while plant-based cheese alternatives less so. However, their acceptance remains low in Europe. Food choice motives (FCM) and trust towards alternative proteins may contribute to purchasing plant-based food alternatives, while other FCM and barriers can hinder this. The present study aimed to investigate whether FCM focused on “Environment & ethics” and “Intrinsic product quality” are associated with behavioural intentions towards plant-based meat and cheese alternatives, and specifically investigating the mediating role of perceived barriers to plant-based food consumption and trust towards plant-based alternative proteins. A survey was conducted in 10 European countries (AT, DE, DK, ES, FR, IT, NL, PL, RO, UK) with quotas on age and gender (N = 7588). Partial Least Squares Structural Equation Modelling (PLS-SEM) was used to determine factors associated with behavioural intentions towards plant-based meat and cheese alternatives. Results showed that “environmental & ethical” motives are positively associated with intentions to consume plant-based alternatives to meat (in 6/10 countries) and cheese (in 8/10 countries). “Intrinsic product quality” motives were not directly associated with behavioural intentions towards plant-based meat alternatives. However, country differences were observed for effects of “Intrinsic product quality”. Perceived barriers to plant-based food consumption and trust towards plant-based alternative proteins play a significant mediating role among all 10 countries. The implications are that environmental and ethical motivations could contribute to effectively promoting plant-based alternatives to meat and dairy. High sensory quality for plant-based meat and cheese alternatives is needed to build trust.