Hodkinson joins the club for an undisclosed fee from neighbours Bootle, for whom he scored 26 goals last season.
He has also netted a further 10 goals for the Bucks during the current campaign.
The 27-year-old has also had spells with Skelmersdale United and Widnes, both of whom play in the Pitching In NPL West Division alongside Bootle.
“As soon as I found out that Marine were interested, I thought it was a no-brainer,” Hodkinson said.
“I didn’t think of looking anywhere else, so I’m made up to finally get it done.”
Meanwhile, Bristol- born Britton has joined from National League North side Chorley.
The 21-year-old started his career at Brislington with Bath, and also lists Waterford and Stockport on his footballing CV.
“I’m delighted to be here and can’t wait to get playing again,” he said.
“It’s been a frustrating six or seven months for me personally, so I can’t wait to get on the pitch, start a few games and score a few goals."
Both could feature for the Mariners on Saturday as they host Morpeth Town in the Northern Premier League.
Photo credit: Marine
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