This train calls at Chesterfield, Derby, Birmingham New Street, Birmingham International, Coventry, Leamington Spa, Banbury, Oxford, Reading, Basingstoke, Winchester, Southampton Parkway, Bournemouth, Brockenhurst, and Poole. In answer to your question, no. Sorry.
There are not many cheap fares to be had on Cross Country. Your best bet is splitting yo ur ticket several times. When Jr. Didcot Red went to Burton last season (from Didcot) he split his ticket 6 times. Reading is now my home fixture. The bus from the station to Madjeski and back is more expensive than my train ticket. I can't use my bus pass on that bus!
It's a tough one for train fares is Reading. You have two options: 1. Split your ticket a few times, this is the best split: http://imgur.com/HnSuW0K - costs that much without a railcard so with your railcard you'll get it down to about £40 2. Look for cheap advances to London from Donny or Sheffield, then a cheap advance - or an off peak day return - from London to reading. Haven't worked it out because the cost can vary massively with advances. As others have said I highly doubt you'll be able to get a cheap advance from Sheffield to Reading. Worth a look though, see what you can find.
Number 2 is probably a better bet. Jr. Didcot Red 2 lives in London & he can get bargains by booking in advance from Paddington to Didcot. Cross Country are probably the he most expensive operator on the network. I am thinking about getting a Season Pass next year once I get to 65 and was planning to alternate between driving and travelling by train. I will need to do some research as fares will,have gone up by another 2.3% on average by then.