I found a flint and, I believe, a suitable stone to make sparks. I get sparks when I hit the flint with the stone but sparks are not big and burn out quickly, I would say before they leave the surface of the flint. I guess I cannot make hotter longer burning sparks using only my flint and my stone therefore I believe I need to find a proper natural easy to burn tinder.
What should I use? Preferably it should be something easy to find in nature (I live in the UK), but for the beginning I guess anything will do. Unfortunately, it is very difficult to find Cramp Balls / King Alfred's Cakes in the area I live so it becomes a bit difficult to find a tinder.
And any suggestions on the technique of catching sparks - as I said previously, they burn out before they leave the surface of the flint. How can I hold the tinder closer to the flint's striking area and avoid messing with the striking stone?
Thanks,

charred cloth. Take old worn out jeans and cut them into 3 to 6 inch squares light them on fire one at a time and deposit them in a tin (I use altoids can) and let them burn out inside with no air. when removed it is the perfect place to aim your spark, from there put it in a nest of small very burnable tinder, ie. a birds nest, or dried grasses bundled and blow very carefully. Takes a fair amount of practice. but definately works in a pinch.

I find the best natural tinder to be cedar bark, birch bark, milkweed pods, dry grass, dry dead tree stumps. Just remember dry and light. Think of things you find in a birds nest. A good tinder bundle should look alot like a birds nest.
Are you using a piece of flint rock or are you using a fire striking rod? If you are using a fire striking rod then it is best to use the back of a knife blade or a piece of hacksaw blade. That will give you the best spark results.

I am using flint rock.

When using flint rock, I have found it best to use high carbon steel for the striker. The one I use was forged from an old file by a blacksmith but, you can use the back of a high carbon steel knife blade (mora knife) or any other high carbon hardened steel. I also make my own char cloth from any 100% cotton fabric (jeans, old tee shirts). I use a pint paint can with a nail size hole in the lid. The hole in the lid is for the pressure that will build up in the can. I cut the cotton material into 1-2 inch squares and place them in the can, put the lid on the can nice and tight and then put it in my grill. It will begin to smoke from the hole. Let it smoke until the smoke starts to become almost clear, about six minutes, it may take a few test runs to get it right. Make sure the lid does not come off of the can untill you are done otherwise the charcloth will burst into flames. Set the can off to the side and let it cool for about ten minutes. You should have usable char cloth. When I am ready to make a fire, I take a piece of char cloth and fold it in half and put it on top of my flint. I then angle the flint upwards, as if I plan to shave my steel. I strike my steel down in a quick movement like a very wide "v" across my flint. I can get a usable ember in one or two strikes. I couple my char cloth with dryer lint and then blow like no tomorrow and voila!, fire.

I've tried to make my first fire with a Swedish firesteel, and birch bark. I must say, that to my surprise it lit verry easy and after that some dead pine needles and twigs catched fire quickly. So I will second the birchbark.

The conditions for my experiment: Dry weather, about 2 degrees Celsius (35.6 Fahrenheit) and almost no wind.

Thanks,
I will experiment with charred cloth. I guess I will go for hiking soon anyway and collect some grass around to check as well. Pity I cannot find my reserves of Cramp Balls, they are such a good tinder...
I have Swedish firesteel and get fire quite easily with it with many natural tinder I can find aaround, but I want to learn to make fire without relying on anything not natural, i.e. no high carbon steel or Swedish firesteel, just rock flint and a stone. However, I can start practicing with not natural tinders in order to increase confidence.
By the way, I tried to make fire using Swedish firesteel and my rock flint - it worked very well!

You might find the movie in the link also interesting.
http://www.bushcraft.se/film/survivalwithmichel-03-quest_for_the_stone.zip