As there's no info about what your PC has to do, it's kinda hard to advise on how you should go about making your decision. At £300 you won't be buying anything super high end, but what your build is skewed towards will have an effect on the advice you receive.
There isn't a strong argument against mini-ITX as a platform these days. If you need multiple expansion slots then it falls down, but otherwise it's really hard to find a scenario where it's not a viable option.
That said, it does come with some inherent disadvantages. Cost can be one but isn't necessarily a concern as it's more of a side effect of a lack of choice. For example socket 1150 boards range from at £45-167 at ITX with around 30 boards on the market (depending on region) and at £30-£150 for mATX with over 70 options available. Those are pretty similar price brackets, but on a budget build any money you can save is helpful. It's worth also pointing out that if you want a motherboard with integrated Wifi (not a bad idea by any means) the minimum price on ITX rockets up to nearly £70.
What ITX does have going for it on budget builds is that most of it's "disadvantages" become insignificant-
■ If you use a H81 chipset for a cheap build on mATX or ITX, you only get two memory slots anyway.
■ Often you'll use a stock cooler so cooler compatibility isn't a particular concern.
■ If you aren't overclocking then case/component cooling is of far lower significance.
■ Lack of support for SLI is a non-issue.
■ Limited SATA ports are unlikely to present any problems.
This can help to offset any potential cost increase if your main focus is keeping things small.
As has been mentioned, the Prodigy case isn't very small - it's noticeably wider than most standard ATX towers and often width is the critical dimension for space saving. Do not consider mATX Bitfenix cases, they really don't convey any benefit over the mITX versions while presenting numerous problems of their own.
If you are on a tight budget though, the NZXT P240 and Bitfenix Prodigy are both perhaps a bad idea. When money is tight, the main place you can save money is the case and you can pick up a solid entry level case for around £30.
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