Little Red are handled by Dnata at LHR. And Jet2 only have their own dispatchers at certain stations. GLA and EDI for example only self handled above wing.
Find a job as a TCO / Dispatcher these days are a challenge. BA don't recruit TCO's externally..
If you want to get into a TCO / Dispatch role with an airline directly. I would start at Check-in or something and wait for an internal vacancy.