Isolating the grids into separate frequency regions is useful with a relatively weak connection but it's not just for system stability and frequency purposes, the losses are lower and above all you have the ability to alter power transfer. If the UK agrees with France for a 500MW export from our end that is nothing more than a few key presses away. They can set a specific export level almost regardless of the prevailing conditions on the AC network with small balancing adjustments in the order of 10's of MW's easy to make. The effect of that transfer will be to make the UK frequency and voltage to drop and the continental frequency and voltage to rise. That will be corrected by the generator governors responding throttling back the continent and raising in the UK.
Reverting to a fully floating state and reversing flow without physically breaking the connection is also extremely rapid.
That transfer adjustment can be done on an AC network with quadrature boosters, but then the losses end to end would be significantly higher and there would be no separation of frequency region.
The original link built back in the 60's did, the 2GW link from the 80's uses thyristors. Fully updated and refitted a few years ago with a new control scheme and uprated power electronics.