Right, we've all gone and screwed up our faces and leapt down the poor bloke's throat…. I think we now owe it to him to try to help!
Jon –
You say you have a "hobby grade" milling machine….
Well, so do many people on this forum – probably, most us, really; either now or in the past. So that comment does not tell us much, but if you identify it there's a good chance someone has the same or a very similar machine so is familiar with what it can and can't do.
"… that would struggle to cut, say, a 4mm groove in steel".
As written that suggests criticising it on sight, but I'll assume you have tried it, and struggled to make it cut the groove.
If so, is the machine actually so small and light that you were trying to push it beyond its designed limits (given its handbook). There are very small mills ones available that seem to have a good reputation, but are intended for fine-scale model-making, clock-making and similar very small work. They'd probably cut a 4mm groove, but only at very gentle rates. Nothing wrong with these machines, but even big industrial machine-tools have their own limits.
Otherwise…
What sort of cutter were you using – and, daft question I know, was it still sharp?
Were you using appropriate speed, depth of cut and feed-rate? (The last is not easy to achieve on a small machine with a hand-wound table, and really only comes with experience with the machine in question – plus at times a lot of patience when you can take only shallow cuts and the far end of the work-piece seems a very long way away.)
What was the material? Did you buy a known, reasonable-quality free-cutting grade or were you fighting something second-hand that was the same colour as any other "pre-loved" steel (grey or rust) but actually some high-tensile or similarly resistant stuff? We've all done it – well, I certainly have.
Finally, what actually was the struggle? Trying to cut the steel anyway, or trying to obtain a good finish without a hedge of burrs along the edges? The groove ending up over-size?