You want a FreeView+ box. Note the "+". These are also known as Freeview recorders and PVRs.
This is a box that plugs into your aerial and your TV and records TV programmes you choose onto a built-in hard disk. The bigger the hard disk (measured in gigabytes, or GB) the more you can record. A 500GB Freeview+ box will record around 250 hours of TV. I've heard that Humax is a good brand for this kind of thing.
These things are a lot easier to set up to record a programme than video recorders used to be. A FreeView+ box will show you a TV guide and you just choose which programs you want to record (most will only record one programme at a time, but some of the more expensive ones will record two different programmes simulteneously). They'll also allow you to easily set them up to record any and all showings of a particular series for instance.
Then you must using some sort of digital receiver to receive the signal. If there is no box then it is probably built into the tele, and yes your aerial should also be plugged in! In that case you could just buy a hard drive. Will have a look now.
Sorry, I meant "aerial cable". The box itself will be about the same size as a DVD player and you'll want it to be near to your TV as you'll need to be able to point its remote control at it.
I can't really advise on which one to get, though. I've heard that Humax is good at this sort of thing but I don't own one so it's not something I can give a personal recommendation on. I've set up a PC to do this kind of stuff because I'm a geek and like making life hard for myself I like being able to tinker.
Incidentally, you might see adverts for FreeView+ HD boxes. The "HD" means it can record the relatively small number of High Definition channels that are available. Personally I wouldn't bother as I'm not sure the small increase in picture quality is worth the fairly large increase in price.
Look for a dual receiver so that you can either record one channel and watch another, or record two channels at once (and, possibly, watch a third on TV!).
Also look for program information. I had an old Freeview box that gave 2 weeks, but the 'feed' contract stopped (with the Freeview box company, not the customer) and we now only get now and next. The Humax ones seem to offer about a week which is much easier for recording as you just go to the program and press 'record', rather than having to add it manually.
You can get Freeview boxes in lots of places, inc Tesco and the above information should be on the box.