Mum Sarah Webster said her children, aged three, six and eight, had all been “really poorly” because of the smell.
The Agency said the the reeking rubbish pile in Great Heck, near Selby, which could contain up to 10,000 tonnes of rubbish - was run by Wagstaff TWM Ltd, which has gone into liquidation.
The agency said it was investigating alleged waste offences and monitoring the odour from the site, near the M62 motorway, that stockpiled mixed recyclable waste.
Ms Webster, 40, said her family had been fighting the stink since June, while the parish council has been battling against the garbage for the past four years.
She said: “The pile is only meant to be two metres high and it is bigger than than. My word it is massive and higher than a house.
“There were some fires and stuff up there recently. We have always had the smell but not as bad as this.
“On Friday night it was pretty toxic, it was awful. I had to lock my gates and when I went out I had to cover my mouth with a jumper.
“It is vile, it smells toxic, at times it smells very plasticky. I am really worried what we are breathing in here.”
It has been estimated that it could cost £1m in landfill tax to dispose of the mound.
Graham Brocklesby, owner of the site, told the BBC: “We need some help... whoever can lighten the impact of the cost that is going to be incurred here.”
No one from the business was available for comment.