With rivers bursting their banks and groundwater brimming at the surface, the additional rainwater will put additional pressure on the underground sewers which are already full.
The firm, which operates more than 67,000 miles of sewers, has been struggling in some areas to cope with the additional water filling up its pipes.
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Tuesday's weather for the west of the region
Tuesday's weather for the east of the region
A further 85 buses are expected to arrive on Tuesday and Wednesday, with officials saying the entire operation will last at least a week.