Your frozen ATPL allows you to sit in the right hand seat of any multi crew aircraft, as long as you hold a current type rating for that aircraft.
The type rating therefore is to teach you everything you need to know to operate that specific aircraft, in a commercial, multi-crew environment. Once you get to the stage in your career where you change fleets, you will have to complete another type rating, or at a minimum, a conversion course for the new aircraft.
While some airlines will pay for your initial type rating, many will either expect you to pay for it yourself, or will pay for it themselves, but 'bond' you to the airline for about 5 or so years. This means that if you leave the airline during this time, you will be liable for the remaining cost of the type rating.
Most people wait until they have their job before doing a type rating, however some people will pay to do a type rating before getting a job, as they are trying to make themselves a better prospects for the airlines. The downside of this is that they have essentially limited themselves to a single aircraft and therefore a smaller number of jobs.
The cost of Type ratings can vary quite a bit depending on the aircraft and, as with everything when it comes to aviation training, there is an expensive way and a cheaper way of doing things, but at the top end of the scale, you could be expecting (or expected by the airline) to pay up to another £20,000 for your first Type rating.