The law is wrong
Because murder is both anomaly (it is highly exceptional: around 600 to 700 instances a year compared to around 1.3 million reported instances of violence against the person) and it is quasi-random – accidental, almost – in when and whether it gets committed.
I'm sure it sounds highly exceptional, but considering that is around double the number of people killed on the roads where speed is a factor in the fatality (factor, not primary cause), things begin to look different. I'm not advocating abolition of speed limits, but given the hysteria around the subject and the overblown policing of the issue relative to its "highly exceptional" nature, the murder rate becomes a more significantly real problem.
Do most murderers "intend to kill"? A good question, since most would claim they did not. What we do know is that the most common method of killing someone in the UK tends to be using a knife or sharp instrument.
I'm going to Mandy Rice-Davis this. Nobody stabs someone with a knife while having the least little concern over whether the victim lives or dies. The act of arming yourself equates to premeditation - they aren't carrying a knife because they're going hiking, in Peckham / wherever. The intention to kill is obvious, and its time the law was tightened to remove this wriggle room around intent. If you stab someone, unless you can prove otherwise, the safest way to proceed is to assume you intended to kill them.
But the outcome (more murders) may simply reflect a growing tendency to carry – and use – a knife than any genuine rise in murderous intent among the wider population.
Carrying a knife with the intent of using it for violence is always an intent to murder. Claiming the violence was self defence simply doesn't cut it (no pun intended).