The BBC approached the other councils throughout the county to ask for an update on their rollout ahead of Monday.
Babergh and Mid Suffolk District Council, where the BBC has also been told some residents have not yet received bins, said it had to deliver 93,000 bins and 180,000 food caddies.
A spokesperson said it was a “huge logistical project” and therefore it was expected there still may be some households without bins.
Dave Taylor, cabinet member for operations at West Suffolk Council, said it had delivered more than 80,000 bins and 160,000 food caddies.
“This has been a major logistical operation, so deliveries have taken place in stages using a contractor and our own waste crews,” he said.
“We are aware that some residents have not received their bins; and we are delivering any missed bins that have been reported.”
Ipswich Borough Council said more than 200,000 new containers for 68,000 properties had been delivered.
“Once residents have had their recycling collected this week, they can start using their new recycling containers straight away,” they added.