This is spot on.

The process is carried out by consultation and negtiation between the train operating companies and Network Rail but in accordance with promises made when franchises are awarded and in accordance with criteria set since the award of a franchise by the Department of Transport (this would take account of constraints set by larger public interest projects such as the West Coast Main Line and CrossRail).

Firstly, Network Rail issue initial restrictions imposed on the network by any planned engineering works.

Train operating companies then calculate best options based on traffic statistics, desired frequencies and taking into account any committments made during the franchising process (e.g. more frequent services or increase in rolling stock units on each service). How the companies do this is up to the operating companies. They presumably use computers to model passenger movements within their franchise. At the end of this process they make a bid to Network Rail for slots consistent with their access rights and committments.

Network Rail then allocates capacity in such a way that conflicts between operating companies are resolved. This could involve balancing high speed long distance with local services, e.g. Birmingham New Street is a notorious problem. More more recently this has become more complex because of open access rights over heavily used sections, such as the London to Wrexham route which lies outside of a franchise. Network Rail use neural network models to plan the best conections between defined nodes on the network but public interest decision criteria based on satisfying maximum passengers are also taken into account.

After a timetable is issued train companies can appeal through a formal process, though as slots are limited this effectively becomes a negotiation over timings and number of journeys.

Once all conflicts have been resolved, Network Rail issues the final timetable.