but at least inside the EU we also got to veto any laws they propose if required.
No, we had a veto in a few, limited, areas.

In the special legislative procedure:
The assent procedure is used to approve certain key decisions such as the accession of new member states, and the approval of Commissioners.
Assent requires an absolute majority of MEPs to approve a decision.
A 'majority' does not mean unanimity.