Somerset Council said the associated road closures and congestion were having a significant impact on collections of rubbish, recycling and garden waste.
Thousands of collections will need to be rescheduled.
Crews will return on Saturday (29 June) and Monday (1 July) for missed rubbish and garden waste, but residents have been asked to bring their recycling and food waste inside if it goes uncollected and put it back out next Friday.
A council spokesperson said: ‘We apologise for the disruption and delays and ask for everyone’s patience as we work to catch up on collections in the coming days.’
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