As the 'person in charge' dealing with day to day operation of the site it is your responsibility to make sure that you are effectively mitigating dust from demolition and construction activity as well as reducing emissions from all machinery.

You should be familair with the Greater London Authority's (GLA) Supplementary Planning Guidance: The control of dust and emissions during construction and demolition and following all the mitigation requirements for your site based on the risk assessment. Medium and high risk sites should additionally be carrying out 'real time' dust monitoring in a transect across the site with supplementary monitoring at any location where there is a sensitive receptor or as required by the local authority.

It is a requirement of the GLA's low emission zone (LEZ) for non-road mobile machinery (NRMM) that all equipment used at your site meets the EU Directive 97/68/EC emission standard. From September 1st 2015 all major developemnts across Greater London will need to meet the stage IIIA standard but there is a higher emission standard of stage IIIB required for NRMM used in the central activity zone (CAZ) and Canary Wharf. From September 2015 the higher standard will apply to the whole of Greater London with NRM used in the CAZ and Canary Wharf required to meet Stage IV of the Directive as a minimum.

You will need to check that the NRMM being used at your site complies with these new regulations, an inventory of all NRMM should be kept on-site stating the emission limits for all equipment. All machinery should be regularly serviced and service logs kept on-site for inspection. This documentation should be made available to local authority officers as required. These NRMM emissions standards will apply to all construction projects which are active from September 2015 including those which commenced before this date. 

You will often also be the first port of call for any complaints from  local residents and businesses and you shoud be aware of the type of pollution being created, their health impacts and how to reduce personal exposure to these.