but still I'm not sure this will stop US missiles 
It will make it a little less likely where the US likes to have allies, so there is collective responsibility.
I think the UK is suffering from war fatigue with Iraq, Afghanistan, Libya and the liberal support for Egyptian regime change. In all of these cases our intervention has led to much civilian loss of live and worse outcomes for who leads the country. In the Middle East it seems to be either strong dictatorships or sectarian violence amongst the various tribes. From the 'uman rights point of view this is bad, but the UK interests are better served by having Western leaning dictators. We live in an imperfect world and as a declining minor power with a small military we cannot put the world to rights and nor should we try to.
Sectarian violence is killing over 1,000 civilians in Iraq every month and this is getting worse, Afghanistan has had a heavy toll on the UK military with many deaths and permanent injuries from enemy contact and IEDs. My money is on that within 12 months of the withdrawal of allied troops it will be ruled by the Taliban again where it is in Iran's and Pakistan's interest for this to happen. Our armed forces have performed badly both Iraq and Afghanistan due to poor inadequate equipment, poor leadership and inappropriate rules of engagement. It has been a case of our troops on the ground (the lions) being led by senior officers and politicians (the donkeys).
The toppling of Gaddafi (to save Sarkozy's skin from where he obtained illegal party funds from him) has led to the widespread looting of his arms dumps and the arming of all sorts of undesirable groups, which have spread out throughout the Middle East and North Africa causing problems which is why French troops are deployed in Mali.
I can't see how our intervention will make Syria better and reduce the number of civilian casualties. If I thought a military intervention by us would make things better I would back it, but on our current record I think we will make things worse. It also doesn't meet the criterion of; does it affect UK interests or threaten the UK, the simple answer to this is no and no.
The evisceration of our armed forces by this current Government has also made us much weaker militarily and the spending of yet more money on an overseas adventure would make this even worse.