Mr Campbell said: “I have not even been accorded the courtesy of a reply to my repeated request to the Turkish embassy in London.
“My meetings with the Foreign Office have proved fruitless despite promises to ‘do our best’. My MP has done nothing to help. I have been left with no option but to seek legal action.
“Anna gave her life fighting for freedom and the rights and lives of others. It is an embarrassment to the UK and a disgrace and shame on Turkey that her body has been left to rot in the rubble of a ruined city.”
Speaking ahead of a BBC documentary in July, Mr Campbell said he will never come to terms with her sudden death but was proud of her.
Mr Campbell said: “One doesn’t really come to terms with a thing like that. I should have done more.
“I thought what she was doing was important enough for her that I could support her by feeling proud so that she didn’t feel like she was out on a limb on her own.”
Mr Campbell added that he urged Ms Campbell not to travel to Syria, as did her friends and family, but said arguing was “futile”.
The YPG, which has about 50,000 Kurdish men and women fighting against IS in the north of the country, controlled the city of Afrin before it was captured by the Turkish military in the week of Ms Campbell’s death.