Okay, so you have school based work experience. However, this is just one week long, and there are several issues that could have occurred: you may not get the position you wanted, you may not enjoy the week and wish you had chose something else, or you may have more than one idea about your future career and obviously can’t do both in one week.
If you are serious about getting this invaluable experience, you can try organising work experience for yourself. This will have to take place during school holidays, and you should inform your teacher that you would be working for a week. However, most teachers will be more than happy to support this use of initiative.
The basis for establishing a place in which to complete work experience is the same as the school’s method: you will need to choose an organisation and write a formal letter asking them if they would be prepared to take you for work experience, explaining that you are doing this outside of the formal school work experience placement scheme and giving your reasons for this. You may feel happier asking a parent or guardian to write a supporting statement, saying that they give their permission and they believe that you will be reliable and committed during the week.
If approached correctly there are lots of places that will welcome you, and it also gives you a chance to make a positive impression. Who knows what the future holds, but you may find them useful to know for a reference or future employment.