A group of 30 Greenpeace activists and journalists detained in Russia since September should be home shortly after Christmas after authorities began on Tuesday to formally process their criminal amnesties and grant them exit visas.

A Greenpeace spokesman said members of the group, who were arrested aboard the Greenpeace ship Arctic Sunrise during a protest against oil drilling in the Arctic, were beginning to go through the administrative process clearing them of criminal charges, before being given exit visas to leave the country. This was likely to take some time, he said, and none of the group were expected to leave Russia before Thursday at the earliest.

The group said Anthony Perrett, a Greenpeace activist who is one of six Britons to be detained, was the first to have the criminal case against him formally dropped. He is now awaiting the exit visa needed to leave Russia and has been told he can collect it on Thursday.

In a statement released by Greenpeace, Perrett said: "It's time to go home, it's time to get back to Wales, and I just got one big step closer." He said the group took peaceful action and he remained proud of his actions.

The 28 activists and two journalists were charged with piracy, later reduced to hooliganism, after Russian authorities boarded their ship. After they were held in St Petersburg for months, initially in prison and then on bail, they were given amnesty under a law passed by Russia's parliament last week, which also granted clemency to the two jailed members of the punk group Pussy Riot.

Kieron Bryan, a British freelance video journalist who is among the so-called Arctic 30, said from St Petersburg: "Only a few weeks ago it looked like we were going to be here well into February and probably beyond. To be getting our amnesty for Christmas Day is pleasing."

Bryan's fiancee was arriving in St Petersburg later on Tuesday to spend Christmas with him, he added, and they would return to the UK together: "Christmas will be whenever we're all together as a family, as far as I'm concerned. It'll be strange tomorrow. Talking to my mum and dad on Skype will be a bit bizarre, but we'll be together before the New Year and we'll start 2014 in the right place, which is good."

Once he returned to his home village in Devon, Bryan said, he would begin trying to put his life back together. "I've got a lot of people to go and say thank you to in person, and do a lot of things I've been missing."

Cliff Harris, the father of another Briton among the group, Alex Harris, said the family were expecting her imminently. He said: "We've been told it might be Boxing Day, but it might not be. I think two have gone through and been told they can leave, but they've got to go before the investigating committee and get the final stamp. It would have been nice to see her for Christmas, but any time is great."

Greenpeace has said Russia was acting contrary to international law in laying criminal charges against people taking part in a legitimate and peaceful protest. The organisation strongly argued firstly for the 30 to be granted bail, and then for them to be allowed to leave the country.