Having found out where the water in the basement comes from, I have finally started trying to solve the problem.
The water comes in through the window when there is heavy rain and the drain backs up enough to come up through the drain in the window box. I've had a look down the drain and it looks like a soak away, but that doesn't make sense because it goes straight down under the house rather than out into the garden. Last night I dug out the plans of the house and sure enough, it is a drain that should go under the house. That means that it is blocked...
I have had a first go at flushing it out with Lars' pressure wash things without any success because it seems to be basically full of soil. I will have another go this weekend, but in all honesty, I suspect that I won't be able to budge it.
I suppose that the next step will be to call someone with a truck and some sort of heavy duty sucking equipment to get all the soil out.
One thing I did learn is that it is best to put the drain flusher into the drain before giving it a test fire.