Just in time for school holidays I've found an offer from Arriva Trains Wales.

Until September, Mondays to Fridays after the morning peak, kids can go for £1 if accompanied by an adult. The details are at http://www.arrivatrainswales.co.uk/kids.aspx but I've seen a printed set which have some more points.

Basically the adult has to have a ticket costing more than £6 and each adult can take a max of 2 kids at £1 per day each. If the adult ticket is valid for more than one day and you want to stay longer the kids need a seperate £1 ticket in each direction.

Not shown on the web but mentioned in the print, most Railcards can be used. So Senior, Young Persons and HM Forces card holders can have their adult discount and take kids for £1. Family Railcard holders can't get adult discount if the kids are using these tickets. What isn't made clear is whether the £6 rule applies to the price of the adult ticket before or after the railcard discount is applied.

Note the headline rule says after 0930 but the small print says that doesn't apply on the most rural routes.

The webpage says "Arriva Trains Wales network" - this extends beyond the Welsh border and covers Shrewsbury- Birmingham International (for the Airport) , the entire mainline Hereford- Shrewsbury- Crewe -Manchester, Shrewsbury-Chester, Crewe-Chester and Chester-Warrington-Manchester. Something else not clear is whether the Kids tickets would be valid on other operators trains on the same route (eg Virgin on N Wales coast, LM between Shrewsbury and Birmingham), I would have guessed NOT but I've checked the Nationalrail special offers directory http://www.nationalrail.co.uk/times_fares/promotions/toc_index.html and those companies are showing this in their company specific pages so presumably they are accepting the tickets on the relevant parts of their routes.