Wow, lots of bad advice in this thread.
Assuming this is for low frequencies, you need to find a honkin great big laminated E core to get your inductor down to a reasonable number of turns. Decent welders usually have large inductors on the output to stabilise the arc current, and very large transformers, so a broken/discarded welder might be a good start. You might be able to use microwave transformers as well, though I suspect you'd need to string some in series to get enough core material for 10mH at 100 Amps.
No. Laminated E core is the worst choice as core geometry goes, and is especially bad for a high current inductor. This isn't iron powder or ferrite, its not some homogenous magnetic material.
Silicon steel is not magnetically isomorphic. It gets much of its flux density from the grain of the metal being oriented with the field. Due to the shape of the core being rectangular, at most 40% of the core material has its grain oriented usefully with respect to the current. This is why the flux density is so low. The amp turns for a required inductance will be the poorest of any steel core because of this. But yes, he would need a honkin great big one, that's for sure. It would be twice the size and have much higher eddy losses than if he were to use the appropriate core for an inductor. Which is a ribbon-wound toroidal core, the kind used in all variacs. 100% of the grain is oriented correctly, and they can handle 2T and per kilogram, will have twice the amp turns for the same inductance as E cores. Oh, and have much lower eddy losses (again, due to the shape). And its easy to find a core that large, you can even buy a commercially available variac with a suitably large core for under $1000.
Decent welders have large split-core
saturable core reactors. If you think you're going to get a core that can take a ton of magnetizing current with out saturating, you're in for an unpleasant surprise. A saturable core reactor is basically a leaky common-mode choke, and sometimes it has a 3rd winding that is used to apply various amounts of DC bias to the core, letting you vary the leakage inductance by putting the core more or less into saturation. Common mode chokes can handle high common mode currents because the AC flux cancels out, and 200 amps could be going through its windings but as far as the core is concerned, there is no current at all. It has some leakage inductance on purpose, often quite a bit, unlike a normal common mode choke. This acts as a series inductor with the load, and causes phase shift. It limits the current by giving the welder output terrible power factor, basically. And the cores are split, there is a seam splitting it in half. This matters because, again, the laminates are not magnetically isomorphic. The split core is split because the grain is oriented in opposite directions for each half, so the amount of magnetizing current such a core is capable of is
significantly worse than a regular E core, and an E core is not the right core to begin with.
And someone mentioned 2.5 meters of MOT cores or something. Are you kidding? Just use a toroid core, its ready made and a practical size =P.
http://www.surplussales.com/Variacs/Variacs-3.html Not in the UK, but most of those would probably work. I think you could get away with the 28 amp one, but you might not. A bit bigger would be best.