At the moment the low hasn't even become a closed off low pressure, but if you follow it through GFS it just 'bombs' going from 985hPa to 935hPa in 24 hours and then deepening to 930hPa.
My advice, which you should take very guardedly and checking with the met office site, remembering that overrules anything I say, and also remembering that things can change rapidly and unexpectedly in weather, so use your own common sense is (sorry about the really poor grammar!):
If you have to travel in the south then do so early tomorrow, the earlier the better or leave it if you can until later on Tuesday. If you are in the north, especially the NW and Scotland then it would be better to travel tomorrow weather wise. What happens on the roads and rail though I cannot forecast, weather is my thing!