Thanks for your reply.
Although I appreciate you had been nominated as next of kin for hospital purposes, this does not give you any extra legal rights over any of your siblings and half siblings.
Whenever someone dies, the person who is legally entitled to deal with his Estate and make the necessary arrangemets over the funeral is either the Executor if a Will had been made or if there was no Will, whoever is appointed as Administrator of his Estate.
Any one of your Father's children can apply to become Administrator. An application needs to be made to any of the District Probate Registry's in England. No preference is given to you just because you were deemed to be next of kin during your Father's lifetime. The appointment of Administrator is done on a "first come, first served" basis so whoever applies first will be appointed.
An application can be made by you either instructing a local Solicitor to deal with the paperwork or you can apply personally to your local Probate Registry. This entails going for an interview and you completing a form confirming what assets and liabilities your Father had.
The Probate Registry will then grant you what is called "Letters of Administration". This is a document confirming that you are the Administrator and is evidence that you are entitled to deal with his Estate and deal with his funeral.
Until you or any other sibling has obtained Letters of Administration, no one of you has the legal right to dictate the funeral arrangements.
I therefore suggest that you contact your local Probate Registry tomorrow to get the ball rolling. Here is a link to find your nearest Registry.
I hope this assists and sets out the legal position.