Imagine a 45 degree line extending downwards from the bottom of the neighbour's foundation towards your land. If your intended excavation does not cut through this imaginary line, then the neighbour's property should be ok without any shoring being required. In this instance, if you are going to be 1.5m away from the neighbour, then as long as your excavation is not going to be deeper than this, you should be ok.
However, this is only a rule of thumb: the presence of ground water and the soil make-up can have a marked adverse effect, in which case support to the neighbour's property would be required. For such instances, there are numerous solutions available, but the most straightforward - soil conditions permitting - would be underpinning down to the level of your intended excavation. This could be installed on a hit-and-miss basis, depending on the condition of the superstructure.
Given the amount of variables that can exist, I would advise you to speak with a local structural engineer, before doing anything.