Daffodils not come up.

Hmmm ... I would have expected "an old flower bed" to drain better than your lawn, to be honest. That suggests that the area where the flower bed was is more compacted then the lawn. Could just be that it is an inch or two lower, so the water runs down to that bit? Worth jambing a form in it every 6" or so to create some holes that might help drainage in that area. A temporary solution, at least.

If they just threw some turf over the old beds, without preparing the soil, I suppose that could be the cause too.

Anyways, turf is lovely consistent grass varieties, no weeds, probably best fenland peat soil and ... all in all ... far better than any grass in your garden or mine, and thus not surprising it sticks out like a sore thumb! Its probably still got 24 months more slow release fertiliser built in to keep it looking lush - and an embarrassment - for some time to come. I'm almost surprised it doesn't clearly show "This turf was bought from XXX" like the core of Brighton Rock!!

 

Do you know where your rainwater drainage goes - is there any chance it's to a soakaway under the soggy area? (and it's been unable to cope with the amount of rain that's fallen in the last few months).