The basic answer to your question is that MRI is not perfect.
To be able to detect all the damage that MS causes, MRI would have to be able to "see" at a microscopic level, but the scanners in the NHS are a very long way from that.
Most MSers have visible lesions on MRI. This is because one of the processes in MS is the formation of patches of demyelination which are about 7mm across in size on average and are normally detectable by MRI. The other main process in MS is axonal death; this happens at a microscopic level which cannot be detected by MRI. Some people tend to have more of the axonal death and less of the lesions. Add to this that lesions vary in size - some are quite small and are easy to miss on MRI, especially with the settings that some NHS scanning centres use.
Neuros have been repeatedly told not to rely on MRI to diagnose MS for precisely this kind of reasons. Unfortunately, many still assume no lesions = no MS. That's right most of the time, but NOT all the time. So history, symptoms and clinical exam results are actually more important than MRI results.