Well if you get all the steel and fastenings etc for free then you may and it's a very slim chance just about do it. . . .BUT . . . It will be compromised in performance and abilty.!
It will require great attention to detail when building to get even moderate accurecy. The inefficiency or the linear rails etc will require more power from motors to overcome any sticktion. Attention to little details of design like adjustments etc will be needed and you WILL constantly be chasing adjustments.

One problem with the bearing setup shown, and I have built like this so speaking from experience here, is that chips and rubbish become a problem with binding bearings. The bearings wear quickly so need replacing often, on upside they are cheap, but still a pain in arse.

To be honest to build anything like a decent machine that's worthy of the effort involved, which to be in no doubt is considerable, then £1000 is the minium needed to make it worth the trouble. If done correctly then your £1000 will earn it's self back in no time and really will be instantly in profit from day 1 as you could sell it for far more than it cost to build.!!

My advise as always in this position is save up and spend that bit more. Even of you buy a chinese router for £500-600 like Eddy suggest's then you'll end up spending £1000 by the time you have replaced the spindle and electronics when they die.!. . . . And they will sooner rather than later.!!