There will of course be an equilibrium, but that equilibrium will be mostly or all English Sparrows and few or no Bluebirds, lacking intervention from man. I have had Bluebird boxes up in my yard for 4 years now; the first two years I had only one box and the Bluebirds arrived first in the spring, built a nest and hatched chicks before the English Sparrows arrived, invaded the nest, pecked the brains out of the mother Bluebird, and built a new nest on top of the carcases (babies just allowed to starve). This is extremely common English Sparrow behavior which might be acceptable except for the fact that English Sparrows are grain eaters and Bluebirds are bug eaters. Since I don't use pesticides I prefer bug eaters, they also provide entertainment by swooping around the mower (which kicks up lots of bugs) when I cut the lawn.
English Sparrows have the same protection in the US as the Norway Rat, killing them is highly encouraged at all times in all 50 states. Don't be fooled by the "English" in the name, they are originally from Africa, but with the help of man have spread to nearly every country in the world. They have caused a dramatic reduction in the Bluebird population here, although the Bluebird population is recovering somewhat due entirely to humans keeping the English Sparrows out of their artificial nest boxes.
After entertaining a brief fantasy of a Bluebird box with a video bird identification system and a guilotine in the door set to chop the head off any English Sparrow which attempted to enter, I put up two more boxes even though there is only enough yard for one Bluebird family. The English Sparrows will preferentially use an empty box if one is readily available nearby. I let them lay a set of eggs and start incubating (so that the mother is reliably in the box in the evening), then I stuff a cork in the entrance, take the box down, empty into a clear plastic bag, kill the mother (just grab and squeeze) and dump the whole nest on the compost pile and reset the trap (put the empty box back up), repeat 5 or 6 times. Since I started this the Bluebirds have fledged sucessfully (last two years) even though there is no noticable reduction in the number of English Sparrows in the yard.
This is not a problem in the UK only because there are no Bluebirds there.
Regards, Glen