Councils will decide next week whether to conduct feasibility studies for the radioactive repository.
Protesters from all over the country carried banners for 2.5km (1.5miles) through the valley of Ennerdale to lobby against the plans.
A petition against the proposals now has more than 17,000 signatures.
Unite, which represents staff at the Sellafield plant, gave its backing ahead of a public meeting in Carlisle on Friday.
Allerdale and Copeland borough councils and Cumbria County Council are due to vote on 30 January on whether to proceed to "Stage 4" of the process that could see the repository built.
The proposed facility could be up to four times the size of Sellafield and take 15 years to build.

Eilidh Doyle won last month's British indoor title over 400m and knows what it take to succeed on the European stage, having won gold in the 4x400m relay and silver in the 400m in Gothenburg four years ago.
Much has changed for the 30-year-old since she last competed at the European Indoor Championships. She's now an Olympic bronze medallist for one.
Having decided against competing in Prague in 2015, Doyle opted to include Belgrade in her schedule this year, and she will again compete in both events.
"Indoors is a bit of a no-no for me, I don't really do it very often," Doyle told BBC Scotland.  "My last full indoor season was in 2013, but we kind of thought this year that we'd kick off the season early, so it's gone well.
"When I did it in 2013, it paid off pretty well. I had a good indoor season but a really good outdoor season as well, it kind of carried through. And that's what we're sort of thinking this year; get a good indoor but really use it for the outdoor which is the main thing."
While Doyle is looking at the bigger picture, with the World Championships in London this summer, she is keen to add to her indoor medal haul.
"Championships are always about trying to get a medal; you want to bring something home," she said. "But I think for me because it is indoors and it is 400m, not my preferred event over the hurdles, it's more of a step to the outdoor season.
"Obviously I want to come here and contend and win a medal but if I run a great time and don't make the podium, I'm not going to be too disheartened. Ultimately I just want to have a great performance, but yes it would be great to bring a medal home."
While the focus is more about performance for Doyle, one of her fellow Scots on the GB team is desperate to win her first senior major medal.
Laura Muir is in the form of her life - having already broken three indoor records this season. Her latest impressive feat came two weeks ago in Birmingham as she set a new British mark in the 1,000m - breaking Kelly Holmes' record from 2004.
Already in 2017 she'd claimed the European 3,000m and British 5,000m indoor records.
Doyle, who like Muir hails from Perthshire, continues to be impressed by her fellow Scot.
"You look at the likes of Laura, she is known throughout Europe and worldwide because of how fast she's ran.
"I think it's great to have Scottish athletes on the map. It's brilliant for the sport and I think it's definitely come from Glasgow 2014.
"There's definitely been a big push in Scottish athletics, there's so many of us that are making teams, winning the British Championships, breaking British records, European records and it's just really, really encouraging."
While Muir targets medals in both the 1500m and 3,000m in Belgrade, she won't be short of Scottish company in either event.
Eilish McColgan is also competing at both distances, while Steph Twell goes in the 3,000m.
Allan Smith (high jump) and Guy Learmonth (800m) make up the Scottish contingent in a 32-strong GB team.
For Learmonth, it's a chance to show he's back at the top of his game after being crowned British 800m indoor champion last month.
Hundreds of people have taken part in a march against the possibility of building an underground nuclear waste site in Cumbria.
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Six Scots are competing in Belgrade, Serbia for the European Indoor Athletics Championships starting on Friday, and there are high hopes for some.