the thing with this 'crap at the bottom of the tank' theory, is that petrol is always taken from the bottom of the tank even when full. If anything when running low it would be crap on top of the petrol.
However, at 1/4 of a tank there is a good 3 gallons in the tank typically. so its not that low really, (assuming the guage is correct).
How old is the car?
mileage?
a fuel filter change might not be a bad idea, at around £12 and a diy'able job. (its located under the car not far in front of the offside rear wheel..