I think if you're mid purchase that is different - it would depend whether it would be the dream house except for the schools, but for me personally, I would certainly consider pulling out if it meant my children would have to go to a sub-standard school.
I think the issue was just flagged in answer to the OP's original question though as to why she wasn't getting viewings. The perception (whether that's right or wrong) that schools are not very good locally would put some potential buyers off.
OP, I've also read your MSE post. You and your partner seem to be quite fixated on getting back the money you have spent on it and the apparent 13% in value on account of the market. As lots of these threads point out, a house is only worth what someone is willing to pay for it. Whilst you had a buyer before, the fact that they pulled out means they weren't prepared to pay the price you'd agreed in the end.
Lots of people have suggested on the MSE post that the £20k you have spent on it (insulation / re-wiring / replastering) may not have added £20k in value, and there may not have been the 13% increase in the market that you think there has. The fact that you both keep referring to putting it on for £345k for a "fast sale" is obviously not working.
I think the choice is to wait for the buyer who will fall in love with the house, not be bothered about paying an uplift of £60k in 17 months, and you can move into your new house (if its still available). The difficulty with that is that if you're not even getting people through the door, you might have to wait a while.
Or if the commute is affecting you so badly, you lower the price to at least get some interest and take it from there.