In New York tonight, Britain’s Prime Minister has set out how £3 million of UK taxpayers’ money will be used to help child refugees from Syria.

This is on top of £5 million of new money the UK is sending via the UN help Syrians through the winter. In fact, the UK says it is the second biggest bilateral aid donor to the Syrian people, with over £38 million pledged so far.

But all this disguises a disqueting truth; that the UK is doing what it can in the absence of many options to do anything else.

For a start, the UK cannot legally arm rebel groups fighting for President Assad’s downfall. This means that every time British diplomats or spies make contact with Syrian rebel representatives in Turkey or the Gulf, they are presumably outgunned by diplomats or spies from other countries promising not just aid, but weapons with which to fight.

These Syrian representatives do not speak with a single voice. If anything, as the numbers of rebels increase, so do the numbers of voices with different demands.

Many have simply given up on a diplomatic solution and just want to be armed; some want foreign military intervention; some don’t. Leverage in these circumstances is well night impossible, beyond exhorting all parties to come together with a strategy which so far eludes them.

The somewhat forlorn hope is that those Syrian groups the west can talk to find that strategy quickly, before surface to air missiles end up in the hands of jihadists beyond anyone’s control who eventually switch their focus to western targets.

Turkey talks the talk about creating a “safe haven”, but until its own national security is sufficiently endangered, its military doesn’t want to become involved in any cross border excursion. And with Russian and Chinese resistance in New York, western countries have almost no leverage – beyond economic sanctions – to force President Assad from power.

The conventional wisdom is that Assad will fall eventually. One British official said earlier this year that he might be gone by Christmas. They are not placing such bets in the Foreign Office now.

(Click on the Snowcloud below for an interactive chart showing the words most used by David Cameron in his speech to the UN General Assembly.)

27 cameroncloud 730 £3m more UK aid to Syria: a measure of our impotence

A Syrian friend of mine isn’t convinced that Assad will be toppled at all, on the grounds that the continuing violence will force frightened Syrians back into the President’s camp. And so the oft-used British phrase that “President Assad has lost legitimacy” needs to be accompanied by another: “nobody else has any legitimacy either.”

Perhaps the defection of senior Syrian officials will shift the regime eventually. Presumably the French and British secret services are doing their best to “turn” as many as they can. But it seems to me that perhaps only horror among the populace of western countries will force their governments to intervene more decisively.

There is no sign of that happening. I often compile tv reports of the latest fighting for Channel 4 News. There was one night recently when I had to choose just which massacre to leave out, because there were too many to broadcast. Yet I suspect that the more such horrific reports we put on air, the more the viewing public thinks “oh how appalling – I am glad we are not there.”

Afghanistan and Iraq have dulled the UK’s appetite for foreign wars, not that we can budget for them now anyway.

Maybe that is no bad thing. But beyond sending medical aid and body armour and telling the world about it in New York, David Cameron’s government is (to quote “Macbeth”) “cabined, cribbed, confined ” – deprived of options while Syrians die in their thousands.

Follow @jrug on Twitter.