Is it true in the days of hand worked operation people use to attempt to board through the last carriage when it was still platformed and the guard use to stay on the platform to try and prevent this.
I do not know the answer (am not quite *that* old) but I can guess, based on personal experience at Stratford where there is cross platform interchange and 'in days of yore' the BR guard (on hand operated 'slam door' trains) would wait until the Central line train's doors started opening to activate the starting bell that tells the train driver to start the train on its way... My being here to write this message confirms that on every occasion I survived the process.
Of course the trains at Gloucester Road would have mostly been stationary (unlike Stratford), which would have made the process about as safe as boarding a bus at red traffic signals!
I suspect that there is a reason why it could be beneficial for the trains to be run this way. By having the train ready to cross the eastbound District tracks minimises delays and therefore enhances track throughput. The converse would be for the Inner Circle trains to wait for a green signal whilst still at the station with their doors open - a passenger who is slow to board (and possibly holds a door open whilst a relative walks as quickly as they can to catch the train) would delay not only this train but also the next eastbound District line train, and at busy times quite likely the trains after that...
Also, its worth remembering that in olden days there could be as many as 40 trains an hour and at such times it was not unusual for the back of one train to be clearing the platform when front of the next train had already entered the station. The trains would be moving slowly, so stopping distances were short. Perhaps the primary reason why trains do not operate in this way 'today' is that when the automated Victoria line trains did this the passengers on the station platforms became alarmed and feared the worst. So to reassure nervous passengers the practise was stopped.
I do agree though that especially on Sundays and other times, when schedules are slightly more relaxed than 'weekday off-peak', it would represent better public relations to have the train wait in the platform with its doors open. Nevertheless, at least (one hopes) the next train will not be 30 minutes later, as was the case at Stratford and why I risked annoying railway staff. Especially in the winter, on a horribly cold windswept platform.