It is also possible it could be a baby wren. They make a loud peep noise too. Amazing that such a sound can come from so teeny a creature. Then again, an adult wren's song is very loud too.
Cacoethes: An irresistible urge to do something inadvisable
I would be willing to bet that if it's a repetitive "cheep".... "cheep" it's a Dunnock or if it's a slightly longer thinner sound, like a "peeeeep" "peeeeeep" that it's a Blackbird. I too have heard both of these sounds and wondered what they were and then observed the birds making them (they are contact calls, obviously not the song of those birds )
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Or maybe a parent robin saying ... 'where the heck have you got to now? I've got a worm for you.'
Gardening in Central Norfolk on improved gritty moraine over chalk ... free-draining.