FatFs f_write not working in LPC1788 Timer ISR
It is usually a very, very bad idea to use FatFS from interrupts. The most common pattern is to acquire the data in the ISR, store is somewhere and have a main loop task that stores that queued data somewhere.

If your SPI driver uses interrupts and you don't enable nested interrupts (advanced topic), then your SPI interrupts won't run until the timer interrupt is done.