The above link says that the Govt of Pakistan made the 3rd request to the Govt of the UK to deport the absconder, former PM Nawaz Sharif. This means that the previous 2 requests were either denied or not replied to.
The former PM was not convicted in politically motivated cases. Rather, he is convicted of embezzlement, money-laundering, and "income without source". He was not handed any capital punishment either.
According to the link
The letter has cited Britain’s own immigration laws of 1974 under
which any person sentenced to imprisonment of more than four years had
to be deported to the country of his/her origin.
Why does the government of the UK think that they should not deport the former PM of Pakistan?
EDIT:
The existing answer suggests that there is no extradition treaty between the UK and Pakistan.
If the UK can deport poor illegal immigrants who went to the UK to earn a few bucks, what is wrong with the deportation of a proclaimed offender who was given a 7-year prison sentence for the embezzlement of public money?