This bird has been in the garden this morning but right over the far side. I shot these images handheld through the window with a superzoom at 1200mm and they are still crops. My initial reaction when I saw the flash of blue was Verditer flycatcher, which we see occasionally.
The first one is unprocessed and seems to show a heavier bill and the wings look dark.
The second image has had some contrast added to try and bring out the differences a little better.
I can now add a 3rd image which shows it seems some white markings on the tail feathers and looks reminiscent of Black-winged cuckoo-shrike but the eye colour doesn't look red.