The neighbourhoods in which people live reflects their social class and preferences, so studying socio-spatial mobility between neighbourhoods gives insight in the openness of spatial class structures of societies and in the ability of people to leave disadvantaged neighbourhoods. We study the extent to which people move between different types of neighbourhoods by socio-economic status in different inequality and segregation contexts in four European countries: Sweden, the Netherlands, the United Kingdom, and Estonia. The study is based on population registers and census data for the 2001-2011 period. For the UK, which has long had high levels of social inequalities and high levels of socioeconomic segregation, we find that levels of mobility between neighbourhood types are low and opportunities to move to more socio-economically advantaged neighbourhoods are modest. In Estonia, which used to be one or the most equal and least segregated countries in Europe and now is one of the most liberal and market oriented countries, we find high levels of mobility, but these reproduce segregation patterns and it is difficult to move to better neighbourhoods for those in the most deprived neighbourhoods. In the Netherlands and Sweden, where social inequalities are the smallest, it is easiest to move from the most deprived to less deprived neighbourhoods. To conclusion, the combination of high levels of social inequalities and high levels of spatial segregation tend to lead to a vicious circle of segregation for low income groups, where it is difficult to undertake both upward social mobility and upward spatial mobility.