The Channel Islands are not British Overseas Territories, but they are a Crown dependency and the Crown does have the power to veto laws created in the Channel islands. Thus are in some ways similar to a Overseas territory.
The island of Sark is a small populated island in the Channel Islands. It has a small Parliament (the Chief Pleas), that also acts as an executive. Prior reform, the Chief Pleas was dominated by the owners of feudal landholdings on Sark, (called "tenants"). There was pressure from the UK government to reform the Chief Pleas and make it more democratic. Sark proposed a Parliament composed of equal numbers of "tenants" and resident non-landowners. The UK Lord Chancellor made it clear that this was insufficient reform, and that the veto would be used, if this proposal were to be formally presented for Royal Assent.
This gives an example of the threat of veto being used to change an internal matter of a Dependency of the Crown, (although not an overseas territory)
Ultimately this ended up in the Supreme Court, as two of the Tenents are the Barclay Brothers, and they wanted to preserve their rights as Tenants. The court decided that the UK government were within their rights to use prerogative powers in this way.