It would appear that you are incorrect - the company which runs the trains is indeed West Coast Trains Limited.
From what I can piece together, this is how it goes:
- The Virgin Group creates a subsidiary company 'Virgin Rail Group Limited' for the purpose of getting into the reprivatised rail market.
- Virgin Rail Group bids for and wins the InterCity West Coast and InterCity CrossCountry franchises.
- Virgin Rail Group creates the subsidiary companies 'West Coast Trains Limited' and 'Cross Country Trains Limited' (i.e. the two Train Operating Companies) to run the two franchises, because they must be operationally separate and to allow Virgin Rail Group to pursue other interests as well as the two franchises already won - such as the high speed rail project (a project which never got off the ground) in Australia which they submitted a bid for in 1998.
- Virgin Enterprises Limited (the part of the Virgin Group which owns and licenses the various Virgin trademarks) creates the trademarks for Virgin Trains, and licenses them to West Coast Trains and Cross Country Trains.
- West Coast Trains and Cross Country Trains commence operations using the Virgin Trains brand name for public purposes, and the companies commonly get referred to by the informal names 'Virgin West Coast' or 'Virgin Cross Country' during the time both companies are operating.
- The Virgin Group sells a 49% stake in Virgin Rail Group to Stagecoach late in 1998.
- Cross Country Trains (aka Virgin Cross Country) ceases operations, leaving West Coast Trains as the only train operating company owned by Virgin Rail Group.
It would appear that the way it goes with the East Coast franchise will be similar - I would be happy to be corrected on the details:
- The company 'Inter City Railways Limited' is created. Regardless of the mechanism by which it was created (not sure if one company created it and sold a stake to the other, or if it was a joint venutre from the start) it ends up being a company owned 10% by the Virgin Group and 90% by Stagecoach - just as Virgin Rail Group is owned 51/49 by the same parent companies.
- Inter City Railways bids for and wins the InterCity East Coast franchise - just as Virgin Rail Group won the other franchises in the 1990s.
- Inter City Railways will either purchase East Coast Main Line Company Limited from Directly Operated Railways or create a new subsidiary company which will purchase the assets of ECMLC Ltd. This company (whether ECMLC or a new subsidiary) will be the Train Operating Company.
- This company will trade under the brand name Virgin Trains or the new trademark 'Virgin Trains East Coast', either of which would be owned by Virgin Enterprises Limited and licensed to the train operating company.
Thus as the new train operating company will trade under the Virgin Trains name, it is correct to say the trains will be run by Virgin, unlike what 455 Driver claims early in this thread. It will not be correct in any way to say that the trains will be operated by Stagecoach, only to say that they will be operated by a company whose parent company is majority owned by Stagecoach.
It is possible that the Virgin Group will attempt to become a private operator on the California High Speed Rail network in the future if it goes to a franchise-style operation instead of being fully owned by the state government as Amtrak California is currently - but early indications are that it will stay government-owned with a new name not linked to Amtrak. If such a bid was done in conjunction with Stagecoach, it could well be that their US rail operations do get run by a new subsidiary of Virgin Rail Group (the 51/49 company) or Inter City Railways (the 10/90 company) or under a new company with a different ownership split.