The closest thing to direct case law is Pretty v. UK, where plaintiff sought the assistance of her husband in committing suicide because of suffering from motor neuron disease. In this case, the issue is that UK law forbids another party from assisting in the commission of suicide. Para. 40 of the ruing says
The Court accordingly finds that no right to die, whether at the hands
of a third person or with the assistance of a public authority, can be
derived from Article 2 of the Convention. It is confirmed in this view
by the recent Recommendation 1418 (1999) of the Parliamentary Assembly
of the Council of Europe (see paragraph 24 above).
and immediately above that
these aspects are recognised as so fundamental to the human condition
that they require protection from State interference, they may be
reflected in the rights guaranteed by other Articles of the
Convention, or in other international human rights instruments.
Article 2 cannot, without a distortion of language, be interpreted as
conferring the diametrically opposite right, namely a right to die;
nor can it create a right to self-determination in the sense of
conferring on an individual the entitlement to choose death rather
than life.
Nevertheless, The Suicide Act 1961 which abrogated the common law criminal nature of suicide is still the law. Parliament has not enacted a law that obligates a person to live.
All medical treatment is performed with consent (including implied consent in emergency cases); UK law say something about the nature of that consent. For one, consent is, necessarily, freely given, so without a special legal mandate that obligates medical treatment irrespective of consent, you have to consent to life-saving or any other treatment. The law allows you to make that decision in advance of the last minute as long as certain things are true (having to do with your medical situation, capacity to consent, proper form of consent). If we leave aside the specifics of advance DNR decisions, no law has been enacted to obligate a person to be treated in order to save their life.
The right to X fundamentally means the right to choose to X, which is different from an obligation to do X. The UK has not enacted an obligation-to-live law, and the Human Rights Act does not mandate that it creates such a law. The act simply says that in interpreting acts of government, the courts must respect the right to life as outlined in Art. 2 Schedule 1.
Incidentally, what the act says is
Everyone’s right to life shall be protected by law. No one shall be
deprived of his life intentionally save in the execution of a sentence
of a court following his conviction of a crime for which this penalty
is provided by law.
Deprivation of life shall not be regarded as inflicted in
contravention of this Article when it results from the use of force
which is no more than absolutely necessary:
(a)in defence of any person from unlawful violence;
(b)in order to effect a lawful arrest or to prevent the escape of a
person lawfully detained;
(c)in action lawfully taken for the purpose of quelling a riot or
insurrection.
