A saw is definitely easier and more efficient for cutting lengths of wood down into fire-sized pieces from a length perspective (I use one of these). However, if there are logs supplied as the original post suggests, they may already be fine length wise. I find the saw is usually only needed when gathering firewood from the forest.

However, whether you need to cut the wood to length or not, you will likely need to split the wood; you need to start small with your fuel to get the fire going. You can do this with either with a hatchet or by batonning with an appropriate fixed blade knife (the latter is more controlled and, I think, less prone to injury for the uninitiated). However, this assumes the logs will be smaller, if they are a larger diameter then an axe may be needed to split them.

I recently came across the following graphic that explains making a fire well:


Source: Scoutmastercg

While this graphic describes gathering fuel of the appropriate sizes, the other method - especially if all you have are logs - is to process the logs into the various sizes with your knife and/or hatchet/axe.

Not really interchangeable tools, one is for turning longer wood into shorter pieces, another is for turning fatter pieces into skinnier pieces. One can do the jobs of the other but it'll be a lot more labor intensive.

However given the level of development in UK you probably don't have much big trees, so maybe axe can do saw's job easier than vise versa.

Are you asking your original saw/ax question from a survival kit standpoint or a camping standpoint?

If you're putting together a survival kit it depends on the area you'll be going. In my area (nothern midwest U.S.) you really don't need either. There should be plenty of hand breakable dead wood. We're not talking about building giant fires for survival.

If given a choice of one - I'd suggest a high quality folding saw - like the Silky or Laplander.

If you want to get a smaller packing store then I'd recommend the Pocket Chainsaw over wire-type saws.

If you're camping, then I'd recommend a bow saw and a long-handled ax. The Boy Scouts have been using that combination for a looong time with great success.

If you want a box saw that stows away, then consider a Sven Saw or a Trailblazer Take Down Bucksaw. The Sven is easier to unfold and use, but it tends to have some sharp edges in a pack. The Bucksaw's tube is less likely to cause damage.

We don't have the huge Northern Boreal expanse forests such as in North America, but we don't do too badly here.

http://www.youtube.com/watch?v=hDfH6CgJ6fM

Denis, you beat me to it. I was about to send that same graphic.

Neither of the above. It is quite possible to start a roaring fire without resorting to either a saw or an ax, at least in environments with reasonable woody growth.

Tinder is the finest and driest wood material available - I prefer shredded juniper bark, pine needles, or pine pitch. Gather small twigs, various sizes so that you have a fuel ladder - a "teepee" formation is probably the simplest.

Gather dead wood of the right size per Denis's very fine graphic. these will be f various sizes. Break them to the appropriate length by (1) propping them against something solid and stomping them or (2) bashing them with a heavy rock (a wonderful primordial experience!)

If you must carry a cutting implement, I would recommend a Sven saw or a solid hatchet like an Estwing model. In a good many jurisdictions, wood fires are obsolete and potentially hazardous. For the same weight, you can pack a small camp stove and fuel which will cook your food faster, with less danger, but also without the undeniable ambiance engendered by a wood fire.

Today I was just shown a fairly incredible amount of damage inflicted by some axe wielding goon on some very nice oaks in one of our local campgrounds. Please engage brain and think before chopping....

If wood is the fuel of choice, get one of the small wood burning stoves designed to make it more efficient. One choice is the Vargo Hexagon Wood Stove but I'm sure there are others. The idea being to contain the flames and heat so you need and use less fuel. Small saw, small hatchet, small wood... I like wood fuel that's already dead, taking an axe to a live oak tree is really bad form.

Following on hikermor's line of thought, it is important to know what is allowable in your area. There are really three different scenarios you could face:

1. You have access and can legally use deadfall for your fire ... for this you can follow the exact method from the image I posted. As hikermor mentioned, this can be done with no tools, but a simple knife might help. That said, a saw and even hatchet (or ability to baton) might be nice depending on the nature of the deadfall you find and how long you plan on having a fire for (bigger stuff burns longer).

2. You only have access to logs or larger pieces of firewood (this can happen in some parks where burning deadfall is not allowed) ... in this case you need to know how to process the firewood into the appropriate tinder / kindling / fuel sizes and have the appropriate tools.

3. You can't have a campfire ... a stove is needed, and maybe a candle lantern for ambience .

Basically, you need to know which situation you are walking into to know how to prepare appropriately.

Here are two of my favourite videos about making a split wood fire:

Part 1:
http://www.youtube.com/watch?v=bfpWthydnDw

Part 2:
http://www.youtube.com/watch?v=sawri36ga1Y

And here's one that explains a twig fire:

http://www.youtube.com/watch?v=Brb4usB35WU