Funeral directors, not unnaturally, aren't too keen on getting stuck in the middle or arguments. (But I'm sure that you won't be the first person to face such difficulties).
I suggest having a discrete word with the funeral director to find out exactly what it was that your father paid for. If he simply paid a sum to cover non-specified funeral arrangements it might be hard to challenge any arrangements that have been put in place using that money. But if he specifically paid for (for example), a cremation with two cars and a jazz band, then it would appear that anything other than that would have to be paid for by the person arranging the funeral. (i.e. his partner couldn't change that to a burial, with four cars and a barbershop choir unless she paid for everything).
Everything that belonged to your father now forms part of his estate. If he'd left a will then the executors would have immediate (but limited) access his estate to deal with any urgent financial matters (such as settling bills). With no will, nobody can touch his estate until such time as they've acquired letters of administration. The only exception would be if the total value of the estate (including any property owned, the car, the timeshare, bank accounts, shares, etc) came to less than £5000. Even then, it's often wisest to obtain letters of administration in order to prove to the relevant people (such as banks or people interested in buying the timeshare) that you have the legal right to control the assets.
Chris