You can integrate MapIt directly into your own websites and apps without having to set up your own MapIt instance!
mySociety runs two public MapIt instances — one with global boundary data from OpenStreetMap, and one with more detailed UK boundary data from Ordnance Survey, ONS, and more.
Their APIs and licensing requirements are documented at:
Both MapIt instances are free of charge for non-profit low volume use, such as by registered UK charities or individuals working unpaid on non-profit projects.
If you don’t fit into these non-profit cases, you will need to get a license. Email the mySociety team at firstname.lastname@example.org with details of your expected volumes, and they will let you know the costs.