Copied from the DEFRA website:
Q34. Can the burial of pet animals continue?
A. Yes. The EU Animal By-Products Regulation allows Member States to apply various derogations regarding the disposal of animal by-products, and, amongst others, the Government has applied the derogation to permit the burial of dead pet animals.
The definition of a pet animal given within the EU Animal By-Products Regulation is 'any animal belonging to species normally nourished and kept, but not consumed, by humans for purposes other than farming'. Therefore, the normal farm species, such as sheep, cattle, pigs, goats and poultry etc. would fall out-with this definition and would require disposal by an approved route other than burial.
NB: Under a strict interpretation of the Regulation there is a case for arguing that no horse should be considered a pet. This is because in the EU as a whole the horse has a rather different status than it enjoys in the UK, i.e. it may be kept for human consumption. The same is not true for cattle, sheep and pigs which throughout the EU may on occasion nominally be kept as pets but do not belong to 'a species normally nourished and kept but not consumed by humans…'.
However, the different status of the horse in the UK provides us with an opportunity to take a more flexible approach to interpreting the regulations where horses are kept as pets, and we have asked enforcement authorities (local authorities) to do this where possible.
Where local authorities decide to advise horse owners that a particular animal may be considered a pet and buried then they will want to give appropriate guidance. Location of the burial site, possibility of livestock access and potential for leaching into watercourses should be taken into account. Useful advice (110 KB) which was provided under the previous Animal By-Products Order 1999 when burial was permitted under defined circumstances remains on the Defra website.
Please note this applies only to England - If you live in Wales, Scotland or Northern Ireland please contact your respective national agricultural departments for advice.
I found this summary of the key points on the Horse and Hound website:
Horse owners must comply with all stipulations made by their local authority regarding the burial site. The authority is likely to state that it must be:
However, each authority may have its own separate guidelines.
Horse owners in Scotland, Wales and Northern Ireland should consult their respective non-agricultural departments for advice.
In England, for more information (tel: 08459 335577) or visit www.defra.gov.uk
Link to the Defra website: http://www.defra.gov.uk/animalh/by-prods/fallen/fallenqa.htm (and the quote above is Question 34)
The relevant department within Bedfordshire County Council was the Animal Welfare section within the Trading Standards Group - whether this is the same for all County Councils, you will need to check.