Many of the warnings are for South Wales, with people being urged to stay alert as downpours mean river levels are continuing to rise.
Some areas could see more than 200mm (8in) of rain by the end of today, and forecasters say there could be a danger to life from fast-flowing or deep floodwater.
One of the areas badly affected has been the village of Aberdulais in Neath Port Talbot where residents were ordered to evacuate their homes due to rising river levels amid reports of the worst floods there for 20 years.
Meanwhile in the town of Crickhowell in the Brecon Beacons national park, where the River Usk burst its banks, some properties were also flooded, with up to 4ft of water.
Pub landlord Howard Baker told Sky News: “The water rose very quickly. The emergency services have been pumping it out.
“The bar area, restaurant area and kitchen is all gone. At its worst, we had 3ft-4ft of water.”
The Brecon Beacons village of Libanus, has already recorded 182mm of rain in just 48 hours – way above the region’s monthly total of 169mm.
Dyfed-Pwys police said some roads have been closed due to a substantial amount of standing water.
There are more than 20 flood warnings for Wales and four in Herefordshire and Cumbria.
A Met Office amber warning – the second highest – is still in place for heavy rain in South Wales until 6pm tonight after starting on Friday.
It said homes and businesses were likely to be flooded, causing damage to buildings.
There is also a yellow warning in place for more heavy rain in large areas of western Britain, covering much of the rest of Wales, as well as parts of Scotland and the north west and south west of England.
Yesterday, torrential rain and winds of more than 70mph buffeted the Republic of Ireland, Northern Ireland and the west coast of Britain.
Thousands of households were left without power and dozens of flights were grounded.
A train in Penrhiwceiber in Wales’s Cynon Valley was stranded as water flooded the tracks.
Sky’s weather forecaster Kirsty McCabe said: “During Saturday, pulses of rain will slowly edge northwards into much of Scotland, while also affecting parts of Ireland and Northern Ireland.
“Central and southeast England will remain largely dry and sunny but it will be windy.
“Despite the breezy conditions, temperatures could reach well above average into the mid-20s. It will be much cooler and fresher on the other side of the rain band in northwest Scotland.
“The rain will continue to push northwards through Saturday night, though it will linger in the far north and northern isles. Later in the night, the next spell of heavy rain will move into central and southern parts of England and Wales.”
For Sunday it will be wet for much of England and Wales, with sunshine and just a few showers elsewhere.
Monday looks fine for most, but another band of rain is set to push east through Tuesday and Wednesday.