Wonder if SWT▸ are allowed to run services on the transwilts?
My understanding is that under Open Access arrangements, anyone can ask to run a train service anywhere. The limitations are in proving that you're suitable to run the service, and it terms of system capacity to carry the extra service.
There are a LOT of loops to be jumped through in terms of setting up a company to do it, as you see with the current Wrexham and Sunderland to London proposals. On the other hand, Hull trains already run a Humberside to London service which in the most part competes with
GNER▸ ... but Hull trains isn't an independent company - it's actually a part of the First group so they didn't have the same loops to jump through - they were already there.
System capacity is the other issue, and an open source operator who wanted to pass through Reading would probably not get accepted. There are other less obvious / less clear cut points like this too.
An Open Access operator into a station run by a franchised company (or indeed a franchise service run by a different operator) is not always welcomed / marketed properly. Indeed, at the time that Wessex Trains ran the TransWilts they very much "camped" in this way, and on more than one occasion I was advised to catch alternative services operated by First (a train to Bath then a bus to Melksham, for example) when there was a perfectly good train sitting there in the bay
for those who knew about it I can understand this "enemy within" attitude from the main player; after all, they are paying the government 1.1 billion to run all the services on top of track access costs and normal taxes, etc ... but Wessex trains was subsidised, and an Open Source operator would not have a premium to pay.
Sorry - did you want a short answer ;-)
Link to even more:
http://www.savethetrain.org.uk/forum/index.php?topic=359.0