Notwithstanding all the previous replies - all of which are sound - and that you may not have fully described what's happening (as you may not have the equipment to test the circuit), I just want to add a couple of points...

1) IF the feed to the extractor comes via the light switch AND you don't want to rewire as has been suggested, then you can use a pullcord-only type extractor (i.e. no timer, no humidistat). Leaving the pullcord switched on will mean that the extractor will operate when the light is switched on. Not very satisfactory, but may be acceptable to you.

2) IF the feed to the extractor does NOT come from the light switch (i.e. it's permanently live) AND you don't want to rewire, then you could use a humidistat-and-timer controlled extractor, ideally with a pullcord too. This would start to run as soon as the humidity rises to a set point, and would switch off when the humidity falls below another set point. The humidity set points are usually adjustable. The pullcord can be used to manually switch on the extractor which would then run for a duration set on the timer (usually adjustable).

As you have bought a fan with and integral timer it needs three wires; a neutral and two lives in order to operate. One of the live wires is a "permanently on live" and the other one a "switched live" that comes on and off with the lights as they are switched. So you should have four wires at the fan position, three coloured and one bare copper, so the wrong cable appears to have been used in the past.

Under normal circumstances the bare copper wire should be sleeved with a green and yellow covering as it is the earth wire, even though the fans are class 2 and do not need an earth connection, the bare copper wire should be curled up and left safely inside the fan not touching any of the other terminals.

From what you describe it's very likely that a cowboy or ill informed DIY-er has put in a standard two core and earth cable and may have been using the bare earth wire as the second live! (This is extremely dangerous).

For your own safety and piece of mind, its probably best to get a Part P registered electrician round to look at this and if need be rewire the section of cable from the light to the isolator switch outside the bathroom (assuming there is one, if not an isolator switch must be fitted) and then rewire from the isolator switch onto the fan itself.

This work comes under part P of the building regulations and is notifiable to local building control and therefore must be certificated in order to comply with the law and prevent any complications or prosecution from LABC should you sell the property in the future. See links below.

http://www.donttakethep.co.uk/

http://www.esc.org.uk/fileadmin/user_upload/documents/public/leaflets/PartP-Web-Oct2012-1.pdf

For fans with timers you require a permanent live, along with the normal switched live and neutral, normally the switched live brings the fan on with the light and then the permanent live keeps it running for the desired time you set on the timer so that after the lights are turned off the fan will continue to run to help clear humidity out the bathroom.
I'd suspect the bare copper wire you can see will be the earthing conductor, it should really have sleeving on it to identify it.

The bare wire is an earth wire and needs to be connected to an earth terminal. It takes no active part in the operation of the fan.

In order to connect your new fan correctly you will need to run an extra live wire to the new fan.
If the old fan was of the pull-switch type then the new live has to run from the light. (This becomes the switched live and turns the fan on and off).
If the fan used to turn on and off with the light switch then the new live needs to be a permanent (unswitched) live, which you can usually run from a joint box in the loft space.
You will need to get a part P qualified electrician to do this however, as this qualifies as a new installation in a bathroom zone.

Hi, the new one will need a permanent live (brown) conductor fed from a three pole fan isolator switch to the new fan along with a switched live and neutral. The bare copper conductor is your earth that needs protecting with green and yellow earth sleeving.

Part P guide - http://www.esc.org.uk/public/guides-and-advice/building-regulations/england-and-wales/

This should be carried out by a competent person as per regulations, it is in bathroom, classified a special location.

The bare copper wire is the earth cable, this should be marked up with green and yellow sleeping and connected to the earth connection in the fan unit, if there isn't one then pop it in a connector block. This won't be why it's not working though, without seeing the new unit it's hard to advise too much but I'd say that the new unit should only require Live Neutral Earth, same as the previous one. If it's on the lighting circuit check it's connected properly at the point where it comes from. To be honest with all respect it sounds as though you are not experienced in electrical works, I'd certainly suggest that before you do anything you maybe get an electrician to take a look, it's easy to get into a mess when at first it seemed quite simple, especially if your struggling to identify Live Neutral & Earth, you may end up damaging existing circuits or your new extractor unit, if certainly get an electrician to pop round and sort it for you, it won't be as costly as you may think and at least you'll know it's done correctly.
Hope this helps
Dan
D H Electrical