Same system up here at my surgery in the NE of Scotland ...... if you don't have your phone in your hand when they open you'll be out of luck.
It's no wonder the fallback is for people to drop themselves on A&E, which then fails to meet it's targets .... the root problem is the failure of the GP system .... no idea how it's allowed to operate as it does (though the fact they're private businesses only contracted to the NHS is a clue) ..... they'd be better cancelling the contracts and creating a large 'pool' of GPs under direct control at local hospitals where you will have the chance to book or just 'turn up and wait'.