Same thing happened to me a couple of days ago - the nest is just outside my back door and there are cats everywhere on this street, so I was dreading it happening as there were 4 babies in a nest the size of a teacup.
I thought of putting it back in, but then worried the mother might reject them all if I disturbed the nest - the other fledgelings might have fallen out in a panic and basically it could have made matters worse, so I brought it in the house away from the cats.
rang my vet

they always take wild birds to a place in Sheffield - rang them - feed it on cat food he said.....rang another place - they had just retired and the RSPCA don't care about anything except dogs/cats I was told

- feed it on cat food again.
So - I put it near the nest again while I thought what to do - and it decided it could fly! not well enough to avoid a cat at the end of the garden though - cat ran off with it! I didn't see that bit - by the time I got to the end of the garden there was nothing to see. Then I saw some workmen cupping something in their hands

have you got a baby swallow? I yelled....They were just about to run it over in their van 'to put it out of its misery'
I took it back in the house and felt very guilty and sad. Left it for an hour - looked dead as it could be - stretched out cold, not breathing. Came back and birdy was sitting up looking at me!
Needless to say she hasn't done well on cat food, or mince as I read on another website - nasty poos and diarrhoea. Then someone I know suggested dried, crumbled mealworms (from pet supplies for wild birds) on scrambled egg - and we are doing well now

see post below about adding water!
my only worry is what on earth to do with her next

She's living in a big plastic box with a furry and very warm hot water bottle (freshened up every hour, fed every hour between 8am and midnight) - she's extremely tame after just 3 days and sits on my glove preening herself....but what do I do with her now?