A property investor has obligations both for the property and towards the tenants.
In relation to the tenant the scope for Responsible Investment could include screening out certain types of tenants (although few funds offer this) or helping tenants to make their operations more environmentally and socially sustainable.
If your charity invests directly in property you are likely to be much closer to the impact of your investment than with equity investment. Engagement can be hard hitting: in a new development, you may be able to influence how it is designed and built. As you are likely to be dealing with a handful of companies, you can also have a deeper engagement with property developers and builders (as opposed to engaging as part of an equity portfolio with a large number of holdings).
Your charity could specifically invest in environmentally sustainable new buildings through the development process and in existing buildings where energy usage and emissions are controlled.