They only had three days to do each dig, but I think that local archaeologists, and volunteers would continue with the digs, finish them up, do the official reports, and then turn over the finds to whatever museum/archives should get them.
There's a somewhat analagous US show called "Destination Unknown" hosted by some guy named Josh Gates. It serves to show the differences in US TV versus UK I suppose. In "Destination Unknown", like "Time Team", they create some premise ("the holy grail might still be out there!") but ulike Time Team, which breaks out shovels and spoons and crawlis in the mud for three days, Gates goes to different exotic spots in the world and pretends to explore unexplored areas (I say pretend because they are almost always in an area where there is a real archaeological dig and I doubt they just said "no, we've never been in there. Why don't you take your cameras and tell us what you find?") But it's interesting for the historical context segments as well as the "Indiana Jones" style hyped up explorer drama.