You cannot be forced to apply for your own job following a reorganisation. However, if you choose not to do so, you will have no chance of being appointed to the position. Consequently, you could end up with no job, and with your employment being terminated.
If this happens and you have been working for your employer for at least a the minimum qualifying period for bringing an unfair dismissal claim (currently a year), you could lodge an application with an employment tribunal.
Your employer's defence against such a claim would probably be that you were dismissed for 'some other substantial reason', a potentially fair reason for dismissal.
If under the reorganisation your previous job content was changed (so the new job was substantially different) and you either did not apply, or were unsuccessful, you might be redundant. In this situation, if you have the relevant 2 years' qualifying period of employment for claiming a redundancy payment, you could force your employer to compensate you for the termination of your post.