As Dis says, it's winter in the UK, on a warm winters day that water is going to be cold enough to be a major issue for a lot of people, if you're not expecting it then even worse.Do we know if the river was cold enough that day to have immediately taken someone's breath away/incapacitate them?
If not, it seems odd that she didn't scream for help. If she did, surely someone would have heard it as it seems like a fairly busy area and a woman's scream would be heard a fair while away. If nothing else, you would have thought the dog would have heard her and jumped in.
If she did fall in the river, it seems like he she was unconscious beforehand or was knocked unconscious as she fell in.
I guess she could have even had a brain anurism/heart attack and just collapsed down the bank and into the river.
A quick google says that the weather on that day was ranging between 1.8 and 6.4c there, which means, yes the water would have been pretty close to freezing.