This depends if you have made a Will, or not:
If there's a Will
The person who’s named as the executor of your Will would have the legal right to arrange your funeral.
This person may be a relative, a close friend and/or a professional such as a solicitor.
You may have appointed several people to be executors to share the list of executor duties when you pass away, which include administration of your estate.
If the executor is a friend and/or a professional, then they would have a duty to pass on your funeral wishes but would probably leave all the funeral arrangements to your family.
If there's no Will
If you haven’t made a Will, then your closest living relative (next of kin) would be appointed as an administrator and would have the legal right to arrange your funeral.
The Rules of Intestacy (inheritance law) would determine who takes on the role of administrator and this is usually in the strict order of: spouse, children, parents, siblings and so on.
If there are two people, such as two children, then a judge would decide who to appoint as the administrator.
The administrator would have the same legal responsibilities as the executor, so they’d have to handle your affairs and administer your estate after you pass away.
The Rules of Intestacy doesn’t recognise unmarried partners. Therefore, if you’re unmarried but have a long-term partner, then they could be left without any say in the funeral arrangements and won’t receive anything from your estate.