Does anyone know where I can get reasonable prices black 165mm cranks? I can only find them for around £100 which seems a bit steep.
If not, my bike has a 13" frame - do you know if its okay to put 170mm cranks on it?

Have you tried Ribble Cycles or Parker international?

If not, there's always eBay!

I've got 165mm cranks on my road bike - the TA Vega - but they are 90pounds.

Other than that try St Johns Street cycles - they do their own thorn short crank (down to 140mm) and slightly cheaper than TA.

And for an even cheaper option look at stronglight cranks - I think they go down to 165mm.

I have a MTB, will these work or do I need different ones?

I'm pretty sure the TA vega cranks can be fitted to a mtb. Might be worth speaking to SJS about their own brand cranks.