Hi Twinfan,
Sorry to hear about the amp. The most likely culprit(s) are the bias resistors having eventually burned out over time on the base of one of the valves. This is quite natural with an older amp. Indeed many 'classic' amps get their unique sound from the fact that many resistors and capacitors have degraded with age.
If any of the resistors (large carbon or wire wound) were to fail due to old age, this would have the effect of sending the bias across the output pair right over to one side, leaving one valve hard on and the other running cool.
Bias resistors age over time, albeit a lot slower than several sets of output valves. They are however cheap to replace.
Switch off the amp and allow a little time for the large electrolytic power supply capacitors to discharge. Remove the valves, and look on the underside of the valve bases, ( I assume the KLIPP is old school hand wired etc). If not, just look for the larger resistors leading off from the base pins on the PCB.
On one valve, you should find a burnt, open circuit, or even abnormaly high resistance resistor(s) compared to the output valve bias components on it's mirror image on the other valve.
If you are fortunate, the undamaged set of components will give you the colour codes/ resistor value(s) and types you need to buy from 'Maplin' to repair the other side.
This advice is not meant to replace the attentions of a 'hands on' tech, but when I was repairing them (many years ago) the above would be the first thing I would look for.
The consolation is that if your output transformers had 'gone' - you would probably have had experienced the acrid smell of burning transformer winding insulation and blasted output fuses.
Regards,
FF.