People are your competitive advantage. Everything else you do can be copied. Maximising your people makes sense on all fronts.
To effect change, look first to your own behaviour. It is pointless to advocate to others when you are not acting in great company style yourself. Be a positive role model.
The most straightforward approach is to the senior team. They make a major impact on company culture, so bring them on board if you can. Present them with the facts general to great companies and specific to your company, and suggest positive next steps.
The HR function can be a great advocate with the ability to make a strong impact. Align all HR actions to great company culture, including your own teamworking.
As a manager, begin to build critical mass. Find like-minded colleagues and look to your way of working. Agree actions for change and keep track of the results. When people comment, tell them what you have done.
If you are a lone voice, work with your own team. Create a great workplace together and show how much difference it makes. Give each other support to continue and celebrate your successes.
As an individual, behave in great company style and you will be a catalyst to others. Network, support and celebrate - by the model you present you can create change.