It really is rather extraordinary that this is the case, but one's next of kin do not have any power or influence unless a LPA has been signed.
Edit for exact (albeit heavily abridged) quote from the relevant Mental Capacity Act 2005:
(9)(1) A lasting power of attorney is a power of attorney under which the donor (“P”) confers on the donee (or donees) authority to make decisions about all or any of the following—
(a) P’s personal welfare or specified matters concerning P’s personal welfare
...
and which includes authority to make such decisions in circumstances where P no longer has capacity.
...
(9)(7)Where a lasting power of attorney authorises the donee (or, if more than one, any of them) to make decisions about P’s personal welfare, the authority—
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(c) extends to giving or refusing consent to the carrying out or continuation of a treatment by a person providing health care for P.