Kymmy ... I don't wish to burst your bubble here but there's no such thing as a 'digital' antenna as such. All that is required is a UHF antenna of the correct group, with the correct gain, aligned to the correct polarity, to match whatever is being squirted out by the local transmitter. What works as a good antenna for receiving Freeview in Swindon, therefore, may not work in Preston. This is exactly the same situation as existed when we were in purely analogue days.
Sven, you need to start checking your whole set-up from the top down. It might be worth asking yourself at this point, why did the previous tenant switch from Freeview to Sky? Possibly because Freeview didn't work for him either? I wouldn't expect the landlady to necessarily know this (or admit it, if she does).
First you need to establish exactly what you need in order to get a good Freeview service in your area. To do this, visit the signal predictor at this website:
http://www.wolfbane.com/cgi-bin/tvd.exe?
Input your postcode and it will tell you which transmitter you can point at, which group areal you need, what gain it must have and the polarity to use.
Once you have that information, compare it with the aerial on the roof. First you have to ensure the thing is the correct group - that would be my first suspicion. You need to identify the colour of the plastic bung in the aerial's nose. The groups and colours are:
Channels - Group - Colour
21-37 - A - red
35-53 - B - yellow
48-68 - C/D - green
35-68 - E - brown
21-48 - K - grey
21-68 - W - black
If your aerial's group does not match the group being transmitted, then there's the problem. The solution is, ideally, to choose an aerial matched to the group your transmitter uses for Freeview. However, this may render it impossible to get analogue services, if those are on a different group. In that case, a wideband aeriel (group W, black) is required. This is where the misconceptions about 'digital' aerials comes from; a wideband aerial will receive all groups but the trade-off is that it has poorer gain compared to an equivalent-sized single-group aerial. So wideband antennas need to be larger to compensate. Most people who have had to swap their antenna in order to receive Freeview have swapped to a Wideband one, hence the tendency to refer to them as 'digital' aerials, even though they aren't.
Of course, it may not be the antenna at fault at all ... can you check the run of coax from the aerial, down the wall (or through the loft)? Look for broken sheathing, or places where two lengths may have been (badly) joined with connectors.
As Kymmy has already said, your booster is also a potential issue. A booster next to the TV will be boosting all the interference picked up by your coaxial cable run, which, if the cable is old and of poor quality, could be considerable. To boost only the TV signals themselves, you need a masthead amplifier that sits right up there with the aerial. Failing that, an amp situated as close to it as possible - in the loft, if the cable comes down that way.
Anyway, go and check on those things, especially your aerial group and gain, and post back what you find.