What are the methods that could be used by the construction industry to mitigate and adapt to climate change? The construction sector at its best is adapting to climate change by making the adjustments required due to the impacts of carbon already emitted. It is also contributing to the mitigation of climate change by cutting emissions to reduce future climate change. The construction sector is a big user of energy and thus emitter of carbon, in its own offices and other buildings, on its construction sites and through the total impacts of what is constructed - it therefore needs to act in a wide range of areas.

Existing buildings are the vast majority of buildings, therefore best practice means: refurbishing to improve all insulation; reduce energy use through use of natural light; use low-energy lighting; use more efficient appliances; change to CHP and renewable energy sources; and reduce water use. Best practice sustainable construction means using one's own buildings and sites sustainably eg ensuring energy and water are conserved well(working with the Carbon Trust and Energy Saving Truston this helps). See the Carillion example here.
Secondly to deal with adaptation to climate change, so far as it allows us to do so. It's important that there is a wide ranging contribution to industry forums, working groups, workshops and so on, to identify best practice and opportunities for adaptation in the built environment. This helps in achieving a full, concerted response to Defra's  Climate Change Risk Assessment 2012 the first official report on the risks of climate change specifically to the UK (see BBC report here).

Getting wide involvement of stakeholders in the built environment in the process of adapting to climate change helps generate more and better solutions. Increased summer temperatures, such as those recently experienced in the UK, can mean overheating inside buildings and around them, so to avoid adverse effects on people's health, concentration and productivity appropriate measures to cool and shade buildings and spaces are required, such as: judicious placement and use of trees; covered areas with open sides.

Increased flood risk, increased risk of drought and more severe storms means making greater use of sustainable drainage systems such as: green roofs; rainwater harvesting; permeable pavements; infiltration trenches; filter drains; swales; basins; ponds and wetlands. Increased pressure on water supplies means water conservation and efficiency at all levels. It's important to design and construct buildings with adaptation to climate change as a planned high priority.