Living in close proximity to an area under redevelopment can be a stressful time for local residents and people working in the area but there are ways of reducing your personal exposure to dust and emissions from the construction activity and machinary used across the site.
The developer will have submitted a dust management plan to the local authority and will be mitigating following a strict set of guidelines clearly laid out in the Greater London Authority's Supplementary Planning Guidance: The control of dust and emissions during construction and demolition to minimise the emissions from the activity and machinery on site.
If you feel that these are not effectively managing to control the dust emissions then you will need to contact the developer in the first instance. They will often have sent contact details to local residents prior to starting work, display them on the site hoarding or may even have a 24 hour telephone number. All complaints to the site should be dealt with by the developer within a resonable timescale, if you feel that this has not happened then you will need to contact your loacl authority's environmental protection team to report the problem.