Belong is a misnomer really, 'ownership' over a deceased body does not exist in those terms for a corpse. Legally there is no tenet for this. There is no legal allocation for 'quasi property' (as it is known) of a body outside the legal rights to burial.
For the purpose of burial only a corpse is considered to be quasi property, rights held by executor and/or next of kin. Once buried a body is considered part of the ground it is placed in and cannot be removed without relevant legal application.
If the issue is the dispute over method of burial it can be complex, last will and testament is not binding in this respect. Right to possession of a body after death is also dependent on circumstance - eg, the hospital may temporarily retain it, the coroner may, then upon release to a named executor, or next of kin via intestacy.
In the above situation the named executor ultimately has responsibility to enact burial as they see fit, regardless of last will and testament or wishes of next of kin, though obviously you would hope these would be taken into account.
With a cremation it is less clear cut, ashes must be collected by the person who delivered the body for cremation as far as I'm aware, as per the contract with the funeral director. Past that point there is still no legal ownership, just possession in whatever form is agreed civilly.
OP should you wish you can view the regulations for burial online by googling them or visiting legislation.gov.uk - Regulation 30 relates to ashes disposal.
If you have a specific case ypu are dealing with then it would be best to speak with a solicitor who specialises. There is a lot of grey area, disputes are famously difficult to solve legally, but you cannot own a body.