Parliament approves

Parliament has approved the beginning of combat operations over Iraq against ISIL, and the Tornado GR4s already in Cyprus will likely fly their first mission very soon from Akrotiri. They have been flying reconnaissance sorties for a while already, along with the first (and for now only) Rivet Joint in service.
There might very well be a SSN already positioned for eventual Tomahawk launches. The RN maintains a SSN(T), with the T standing for TLAM, Tomahawk land attack missile, east of suez at all times, and it could fire its cruise weapons from the Gulf. Another could well be in the Mediterranean, too.

There will be time to talk in greater detail about the british operations and contribution to this fight, which doesn't have a clear end in sight. Tonight it is time to wish for happy hunting and for a safe return for everyone that will be involved.

The little that can be said right away is that already it looks like the most precious contribution that can be made will be tanker support, as well as ISR support, both in extremely high demand.
Combat aircraft are likely to be relatively less important, in a way. First of all, they are going to be few in number: the talk at the moment is for 6 Tornados, and it is going to be hard to do more, since the Tornado force is down to just three frontline squadrons, and of these one is ramping down ahead of disbandment next year (II (AC) Sqn), another has just returned from its last Afghan tour (IX Sqn) and one has just deployed in Afghanistan (31 Sqn). Add the Tornado deployed to Africa to support the ISR campaign to locate Boko Haram and the kidnapped girls in Nigeria, and the overstretch is evident.
Typhoon will have to be used, if the Iraq effort is to be ramped up. But Typhoon, as we know, is still years away from the much needed full air to ground capability, so there are many limitations, ifs, buts and maybes.

Another factor in limiting the reach of the air campaign is the distance of flight and the need for air refueling. France's own 6 Rafales, for example, flying from Al Dhafra, only fly one mission a day, roughly, tipically with two aircraft, even if double pairs have also been used. Each mission takes several hours and several AAR contacts. France has only one KC-135 tanker assigned to the operation, named Chammal, so it is very much dependent on coalition tankers, mainly USAF ones.
The USAF has been flying over 30 tanker sorties per day, and in the relatively short time since the beginning of the operations, CENTCOM has already registered a staggering 1289 tanker sorties.
The number of air strikes compared to the sorties flown is very low: only a few more than 200 airstrikes, with some 350 weapons expended in Iraq, and even less in Syria. The need for tanker support will only grow greater as the fixed, known and static targets are taken out and the focus shifts more and more to hitting mobile and relocatable targets. This will require aircraft to loiter and to hunt for targets, and will require endurance and lots of fuel. Plus, of course, even more ISR to locate the targets.
The RAF might be able to provide a Sentinel R1 to aid the ISR effort (difficult to say the least, since one is in Africa and Afghanistan still calls for Sentinel surveillance as well, which means a forward fleet of 3 machines is already well busy as it is) and some Voyager. There are 9 Voyager in service, but one is for air transport only and one is in the Falklands. When the QRA tanker requirement at home is added in, it is evident that there isn't much to go around in this field either. 
The options, in any way you want to look at it, are limited. 

Main air bases for the campaign. Approximate positions only. Incirlik is a NATO base, but Turkey is not granting authorization for its use for combat operations, at least for now. Not clear if RAF aircraft from Akrotiri will fly over Syria despite the risks this implies and despite the political hesitations. Curving south over Jordan or north over Turkey, on the other hand, only add more distance.

The overall responsiveness of coalition airpower to developments on the ground is, at this stage, still quite slow for obvious reasons: one major difference could be made by forward basing inside Iraq. The US intend to deploy aircraft to Irbil, and these will have much better chances to provide endurance and responsiveness over Northern Iraq. Of course, this does require boots on the ground, which the US already have in hundreds, with an Army Division HQ also on the way. Super Hornets coming from the USS George W. Bush (CVN 77) can also compensate the tiranny of distances somewhat, and some help comes from the USMC Harriers of USS Bataan and USS Makin Island as well.
The USAF has employed B-1 bombers as well, which have huge range and endurance, and they are likely to account for a big share of the USAF contribution so far in terms of strikes and ordnance dropped.

The start of RAF ops comes together with the announces that Belgium is to contribute 6 F-16, Denmark 7 F-16 and the Netherlands on Wednesday promised 6 F-16 plus two spare aircraft to the Coalition in one week's time.
To all of the men and women involved, again happy hunting, and wishes of a safe return.