My husband won three grand in the Dickinson's Real Deal Competition once. He did the online entry rather than the phone-in though - as far as I know, they only do the phone-in now.
As to whether they'd keep calling if you were out, I'm not sure how you'd know unless you were the person who did the calling, rather than a winner. I do know that when Real Deal rang, they told my husband that his name would be up on the program's website in a couple of hours (and it was), so I suppose not having put it up already gives them room to contact someone else if you don't respond. I'd like to think that they try more than once before moving on, though.
I did once win a pair of tickets to watch England play at Wembley. It wasn't a TV competition, it was a football website comp, and when they rang to tell me they said that they'd draw another winner if I couldn't use the tickets. I really wanted to go, but had no transport and didn't want to see the tickets go to waste so I asked them to ring me back in half an hour while I tried to sort something out. I never really expected them to, but they did, by which time I'd arranged with my son to take us up and we got to watch the game together.