The latest Kantar figures show that Bradford-based Morrisons' sales fell 2.9 per cent in the 12 weeks to December 1 and Leeds-based Asda's sales were down 1.9 per cent amid the uncertainty of a General Election, a lacklustre Black Friday and a wet autumn.
Fraser McKevitt, head of retail and consumer insight at Kantar, said: "It's a continuation of what we've seen in recent months at Morrisons.
"We still see that the average basket size is getting smaller at Morrisons, which has been the thing for a while.
"It just seems that it's looking a bit lacklustre and they've been the slowest growing of the big four since July."
Analyst Bruno Monteyne at Bernstein said: "The weaker Kantar trend for Morrisons continues, where they continue to be the worst-performer of the big four peer group.
"The trend for Morrisons is worrying and has been bad for a while now."
Mr McKevitt said it has been a difficult time for Asda, but there are some more positives.
"Where they are finding life hard is there is a lot of competitive activity out there," he said.
"This time last year Asda did a lot of beers, wines and spirits deals that aren't necessarily being repeated this year.
"There are more promotions available in Tesco, both through the 100 years of value campaign and they are putting a lot of effort behind the Club Card Plus activity.
"Asda are lapping a strong last year, but there are some positives - double digit online sales growth and their premium lines are still doing pretty well."
Mr McKevitt expects both Morrisons and Asda will see a pick up in sales over the coming weeks.
"In December, we always see the big four getting a greater share of sales than at any other time of the year, but I'm sure we're also going to see great growth rates for Aldi and Lidl and they will be at their highest ever Christmas share," he said.
"I think everyone will be claiming they have done quite well.
"The reasons people revert to traditional supermarkets at Christmas is that they offer the wide range and the discounters' business operation is based on fairly limited stock.
"For many people that seems to work quite a lot of the time, but if they need to get a particular jar of cranberry sauce or a particular something for their Christmas table, they are not going to get it in one discounter in one trip."
Kantar said total sales growth at the UK's grocers slowed to 0.5 per cent over the three month period, with consumers making one less visit to the shops on average than this time last year.
All of Britain’s big four supermarket groups recorded sales declines over the period and lost market share to the German discounters Aldi and Lidl.
Sales at market leader Tesco fell 0.8 per cent over the period, while Sainsbury’s saw sales declines of 1.1 per cent. In contrast Aldi’s sales rose 6.2 per cent and Lidl’s rose 9.3 per cent, although much of this was due to new store openings.
When asked whether shoppers are holding off until the General Election is out of the way, Mr McKevitt said: "I don't think anybody is going to be holding off specifically for the election.
"I might have anticipated growth to start creeping back up in the sector. It's hard to pin it down, but I don't think the weather, General Election uncertainty and Brexit uncertainty have helped.
"The other thing is price rises in grocery are only running at 0.8 per cent like-for-like at the moment, although that is good for the consumer. All those things combined have made it a fairly downbeat run up to Christmas."
The number of people taking advantage of Black Friday this year fell to 53 per cent from 57 per cent last year, with signs of "promotion fatigue" among consumers, an increased scepticism regarding the value of the deals on offer, and some retailers pulling back from the day all together.
The event is always less significant in the supermarket calendar and this year only 5 per cent of Black Friday deal-hunters bought something from a grocer.
Mr McKevitt said: "Fewer people are taking part than they did last year.
"People are saying what they wanted to buy wasn't on offer and they weren't necessarily trusting that the offers that were out there were actually real and were offering good value.
"There was a time when people thought this is a great time to get a bargain, but I think now people believe well I can just wait a bit and there will be as good a deal coming along."