This paper considers estimation of disease prevalence for small areas (neighbourhoods) when the available observations on prevalence are for an alternative partition of a region, such as service areas. Interpolation to neighbourhoods uses a kernel method extended to take account of two types of collateral information. The first is morbidity and service use data, such as hospital admissions, observed for neighbourhoods. Variations in morbidity and service use are expected to reflect prevalence. The second type of collateral information is ecological risk factors (e.g., pollution indices) that are expected to explain variability in prevalence in service areas, but are typically observed only for neighbourhoods. An application involves estimating neighbourhood asthma prevalence in a London health region involving 562 neighbourhoods and 189 service (primary care) areas.