We found out about this incident on a facebook group for Old Tunbridge Wells where the above photo was published we then done some digging and found the South East History History Forum which gave us some more images and reported what the press had said, which we have copied below
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Press cutting below from the local paper
FROM OUR CORRESPONDENT TUNBRIDGE WELLS, DEC. 22 
​The driver of a diesel electric train had a remarkable escape from serious injury when his train collided with the rear of a stationary diesel electric train in Tunbridge Wells Central station shortly after 1 p.m. to-day. Eighteen people were admitted to hospital. The stationary train, which had travelled slowly from Hastings, was waiting to link up with the second train, also from Hastings, to form a fast train to Charing Cross when the collision occurred. The main Hastings-London line was still blocked at midnight. Railway workers used crowbars to free the driver of the second train, Mr. Charles Giles, aged 62, of Church Down, Bromley, from his wrecked cab. He escaped with lacerations of the scalp and left cheek. With two passengers he was detained in hospital. The others were Mr. William Cross, aged 75. of Ashley Gardens. Rusthall, Tunbridge Wells, who had minor injuries and Mrs. Janet Burr, aged 61, of Croft Road, Hastings, who suffered concussion. The condition of all three was described as comfortable. Another passenger, Mrs. Mildred Muckleston, aged 70, of Hill Street, Hastings, who had fractured ribs, was discharged from hospital to the care of her daughter. The others taken to hospital were discharged after treatment for cuts and bruises. Many other passengers were given first aid for minor cuts and shock on the platform.​

The Evening Standard, 22nd December 1958
TRAINS CRASH - 22 INJURED. 

​Collision in station at Tunbridge Wells. Two diesel-electric trains from Hastings crashed in Tunbridge Wells Central station at five-past-one this afternoon. Twenty-two people were hurt and the line blocked. Fire broke out in the crushed driver's cab of one. The trains were the noon slow from Hastings and the 12.20 fast. At Tunbridge Wells they were to be joined in one train to Charing Cross. "They came into heavy contact while being coupled," said a Southern Region spokesman. The driver's cab was crushed and the motorman injured. Fire started but was extinguished by firemen who were called. Motorman Charles Giles, aged 62, was taken to hospital with head cuts. He was detained for an X-ray.Eighteen passengers, some from Hastings, Bexhill, St. Leonards, and some going to Ramsgate, were also treated in hospital. Two were detained - Janet Burr, 61, of Croft Road, Hastings: and William Cross, 75, of Rusthall, Tunbridge Wells. Three others were treated on the station for shock and bruises

​From the Railway Magazine, February 1959:​'A collision between two diesel-electric trains occurred at Tunbridge Wells Central Station at about 1 p.m. on December 22. A six coach set, which had called at all stations Crowhurst to Tunbridge Wells, was standing in the station, when it was struck by the incoming 12.20 p.m. fast train  from Hastings, to which it was to be attached. The motorman of the second train and two passengers were detained in hospital, and several other passengers suffered minor injuries and shock. Mr R.W.Doust writes that by 3.30 p.m. the coaches of the stopping portion were removed under their own power, although only the leading motor could be used ; they were berthed in the sidings between Tunbridge Wells and High Brooms. Shortly afterwards, a breakdown train, hauled by "C" class 0-6-0 Nº 31037, arrived from Tonbridge. The main frame and side of the driving cab of the 12.20 from Hastings had been buckled out over the platforms, and were fouling the loading gauge of the tunnels at either end of the station. After the sides of the cab had been cut away with oxy-acetylene equipment, the damaged portion was torn off completely by means of chains attached to the locomotive of the breakdown train. Considerable difficulty was experienced in removing the buckled section of the main frame, but eventually the coaches were hauled by a locomotive to the sidings at Tunbridge Wells West Station. Meantime the down line was re-opened for traffic at 6 p.m., and normal services were resumed the next morning. Mr. Doust adds that this probably is the first occasion on which a diesel train has been seen at the West Station'.