No, the area isn't waterlogged. I did look at willows but I realised yesterday that the area is not far from the septic tank and I worry that the roots could cause damage to that or the piping. I'm thinking Alder in that spot now and probably Guelder Rose close by where I plan to grow a hedge.
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https://www.woodlandtrust.org.uk/trees-woods-and-wildlife/british-trees/a-z-of-british-trees/guelder-rose/
Gardening in Central Norfolk on improved gritty moraine over chalk ... free-draining.