The International Criminal Court (ICC) does not consider the austerity deaths in Greece as crimes as defined by the Rome Statute—so it is unrealistic to expect the Court to seriously consider similar complaints against the British government.
An investigation into multiple breaches of Human Rights law in the UK is the jurisdiction of UK's human rights bodies and the UK legal system, particularly the Courts. The UN prefers that domestic remedies be exhausted before filing complaints with the Office of the High Commissioner for Human Rights (OHCHR) in Geneva, Switzerland—which I have been reporting to on a frequent and voluntary basis since January 2012.
Every four and a half years the UK’s human rights record is considered by the other countries which are members of the United Nations Human Rights Council in a process called Universal Periodic Review (UPR). UPR is based on the UN Charter, the Universal Declaration of Human Rights and all UN human rights conventions to which the UK is party.
See http://www.twitlonger.com/show/k7lk42 and http://crimesagainstgreeks.com/attachments/article/51/EM_T04_OTP-CR-47_12.pdf