Water Leaking Out Of Dispenser Drawer On Spin

So, my washing machine has, in the past few weeks, decided that our favourite washing programme should involve the machine spitting out heaps of water through the dispenser drawer during the spin-phase of the programme.

We use programme "E" which usually includes wash, rinse, empty and spin. However it seems to be missing out the 'empty' stage, meaning that the spin stage occurs with the machine filled with water, and for some reason this causes it to come out of the dispenser drawer onto the kitchen floor.

So in order to wash our clothes we have to put it on this cycle, listen carefully for it to start its spin cycle, once it starts the spin run to the kitchen and cancel the programme, then go to the manual settings for emptying and spinning. This is extremely frustrating as we occasionally don't catch it before it starts spinning, leaving a wet mess to clean up, and it means we can't have the washing machine on unsupervised (i.e. during the night, while we're out, or just when we want to do something else rather than sit watching the machine for 2 hours).

Any suggestions for what the problem could be?

We've had to phone the letting agency about 3 times about our washing machine so far, and we've only been in this flat 6 months, and we're a bit worried that they're just getting sick of us now - particularly the landlord who probably loses money everytime the letting agents need to send out a washing machine technician, so we're a bit wary of doing it again and if the problem is simple enough, we'd love to be able to fix it ourselves. Particularly as our fixed-term contract has now ended and we're here on a rolling contract which renews on a monthly basis.