This question really isn't about the airstrikes and civilian casualties. Nor it is about the arms sales to Saudi Arabia. These are real concerns, but similar to those found in many other conflicts.
But, according to the UN, there is a famine brewing at larger scale than Ethiopia some decades back. This apparently is largely due to the Saudi coalition mounting, in effect, a naval blockade.
Why is this blockade not getting more strongly condemned by the US and the UK, even if Saudi Arabia is allowed leeway to pursue the rest of the conflict as it sees fit?
I can think of no recent counterinsurgency war in which a policy of subduing a country via large scale blockade, including food, was pursued. Imagine the outcry if the US had tried doing so in Afghanistan or Iraq. I am pretty sure the USSR did not do so in Afghanistan either. Nor France in Algeria or the US in Vietnam.
The only conscious starvation policies I can think of are WW1 Allies blockading Germany and the WW2 German UBoat campaign against the UK.
If the UN's and the NGOs' warnings are justified, and millions of civilians' lives are at risk, it seems in our best interest to disassociate ourselves from Saudi actions. Letting alone the direct human misery caused, that level of suffering will inevitably lead to further radicalization, just as the Chechnya wars have spawned numerous extremists.
In the short term, Saudi Arabia has little choice but to keep purchasing weapons from its usual suppliers and to keep pumping out oil, so their leverage in pushing back to have their way wrt the blockade seems limited.