You can use another TOC with your existing ticket if you are instructed or permitted to use another TOC by a member of rail staff - although sometimes you will not manage to get anyone to do so even if you've missed the last train through no fault of your own. However, there is still a general duty on any Train Company which is in a position to do so, to assist you by arranging alternative transport (e.g. taxi, inter-TOC ticket acceptance) and/or overnight accomodation, as required. If any Train Company, having been in a position to help you, refused to do so, then you would be entitled to recover your reasonable costs of alternative transport (e.g. new interavailable ticket, taxi fare - shared where practicable) and/or overnight accomodation from them.
The above advice is contingent on you having left at least the minimum connecting time for each interchange station in your planned itinerary - this is usually at least 5 minutes for smaller stations, up to 15 minutes for the largest stations. This time can be found either on
www.brtimes.com or by consulting the National Rail Timetable published on Network Rail's website.