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Possibly (if the children were early teenage girls) one of them was placed ("billeted" was the word) with my family in the town for a period. As you might imagine there was an element of friction; nobody, on all sides, quite knew what to do. Known in the family as "the evacuee". Places were found to insert them at local schools. After a few weeks of nothing happening, many London parents came and took their children back, by normal services.
The trains for them were fully specials, not by the normal services. As described above they were typically made up of suburban type vehicles, without corridors through the coach (or toilets). Those were still pretty standard at the time, even on medium distance services or summer excursions. The route would have been most likely the way the main expresses went, and still do, they would be unlikely to have routed via Bristol, where there were enough issues of their own. A number were hauled by freight locomotives - it was still "summer" to the railway and trains were not heated. The time taken from Paddington (or possibly Ealing etc) would have been likely double what the normal express took; they were run as "Control Extras", which is a professional railway expression for "make it up as we go along". I believe they stopped every couple of hours at stations which had toilets on the platform, and where, if they had managed to get organised, local groups like the Salvation Army issued sandwiches and water. The driver and fireman would have reported, taken the carriages to the starting point, taken the children to destination, and then taken the carriages back to London. If they did a 16-hour day or more, so be it.
The well-known luggage labels attached to the children were typical railway ingenuity, it was all they had to hand in quantity at the starting station, it having been recognised that there might well be separation.
Incidentally, Mr Taunton Senior, not having met yet the future Mrs Taunton Senior, took one look at his own home station elsewhere on his morning commute, with all the children milling around with luggage labels in their coats, was appalled, and on his way in to the office went via the military recruitment office, joined the queue of others, and signed up, that day, although not actually taken in until later.