The 1.4GW Fab Link and the 1GW IFA2 link would connect France with the UK's national grid. And the 1GW Viking cable would carry energy between Denmark and the UK.
Each cable would be installed by 2020 and carry energy between the countries. Interconnectors are designed to increase the availability of energy, thereby reducing costs.
The projects were submitted through an Ofgem regime for near-term interconnector investment. Five proposed cables qualified to be assessed under Ofgem's programme.
Also included in the regime was the NSN Link with Norway that was approved by the Norwegian government in October and was assessed by Ofgem in December.
A fifth interconnector would have joined the UK with Ireland via the Greenlink cable. However, the proposal failed to demonstrate its cost effectiveness. Ofgem said it was still consulting on the application but was "not progressing" it.