Like was said earlier, if it can be seen, to any extent, from a public place, then it is an offence under the LItter Pollution Act 1997. The Co. Co. would persue this.
Also, an EHO (contact the local HSE office for contact details) will have an issue if it is likely to be a risk to human health, and if it is attracting vermin.
If it can't be seen from a public place, then it can be dealt with under the waste Management Act 1996-2007, as it is illegal to store waste without a permit (and in such cases, it would be assumed to be an inappropriate situation).
In some local authority areas, there are Bye-laws which require the presentation of waste to a collection service, and therefore, by not presentating their waste, these people are in breach of the bye-laws, if there are any.
Get onto your County or Borough/Town Council, and ask for the waste enforcement section. The people responsible (occupiers) can be served notice under section 55 of the WM Act, to remove the waste, and to ensure that there is no further inappropriate storage in future.