About the cheapest ones I know of are the Zyxel NSA-310, NSA-320 and NSA-325. The NSA-310 is a single drive unit, the 320 and 325 are dual drive NAS boxes.
You can get the
NSA-310 from CCL for less than £40 delivered. Add a 2TB drive (around £70) and the total is around £110.
It runs LMS 7.7.1, it doesn't come pre-installed, but is a downlodable package (you can download and install it from the NAS admin web pages).
It's not the fastest NAS, but is easily up to running LMS and streaming to a few squeezeboxes. It's also a little noisy (has a fan).