Acts as a 5'-hydroxyl kinase, a 3'-phosphatase and a 2',3'-cyclic phosphodiesterase. Catalyzes the transfer of the terminal phosphate of ATP to the 5'-hydroxyl termini of ribo- and deoxyribonucleotides. In the presence of ADP the enzyme also catalyzes an exchange reaction. In the exchange reaction, an excess ADP causes the enzyme to transfer the 5' terminal phosphate from phosphorylated DNA to ADP (PubMed:5323016, PubMed:199248). Involved in countering a host defense mechanism which activates T4-induced anticodon nuclease and shuts off viral translation. The polynucleotide kinase modifies the ends of nicked tRNA generated by the antiviral response of the host bacteria and facilitates repair by T4 RNA ligase (PubMed:2444436). a 5'-end dephospho-2'-deoxyribonucleoside-DNA + ATP = a 5'-end 5'-monophospho-2'-deoxyribonucleoside-DNA + ADP + H(+) a 2'-deoxyribonucleoside 3'-phosphate + H2O = a 2'-deoxyribonucleoside + phosphate Optimum pH is 6. Homotetramer.