In addition to the amber warning, there is a yellow Met Office warning for rain that covers a larger area of Wales and south-west England, which came into force at 18:00 GMT on Monday and is in place until 18:00 GMT on Tuesday.
Between 20-40mm (0.8-1.6in) of rain is expected widely with up to 80mm (3.2in) over Dartmoor and the higher ground of Wales.
The Met Office suggests there is a small chance of up to 100mm (3.9in) on the more exposed and prone hills.
More yellow weather warnings for rain will cover north-west England until 15:00 GMT on Tuesday and central Scotland from 06:00 GMT to 12:00 GMT on Tuesday, where a lot of rain could fall over a short period of time.
Up to 80mm (3.2in) is expected over the Cumbrian hills in particular which could lead to some flooding.
The main area of rain will clear away to the north-east during Tuesday but rain and strong winds are likely to continue especially across Scotland into Wednesday.
Over the last few months the UK has seen Storm Benjamin and Claudia, which were named by France and Spain respectively.
So far we have only experienced one storm named by the UK Met Office and our storm naming group – Storm Amy. That is why we go back to the ‘B’ name – Bram – on the UK, Ireland and Netherlands storm naming list.
The next storm after Bram would be named Chandra if medium or high impacts are expected.