Houses need TLC and maintenance to function.
This includes cleaning the gutter and your surmise could well be correct.
However...
The dormers in houses are seldom detailed correctly for interstitial condensation.
The provisions of Part F can be dispensed with for small roofs and many people seem ot think this includes dormers.
"For the purposes of health and safety, it may not
always be necessary to provide ventilation to small
roofs such as those over porches and bay windows."
An argument can be made that a dormer is just a roof-level bay window, but in my opinion, this can prove unwise in practice, because as the most exposed windows in the house they are more prone to the effects of inclement weather.
That having been said, single dormers without extension flat roof elements normally serve well, and the problems are less likely to be interstitial than to be to do with how the junction of the dormer and roof is sealed and weathered.
The choice of concrete tiles may not be the best to give good sealing.
Sexy minimalist details work with slate or smaller plain tiles or shingles, but larger profiled concrete tiles can be difficult to work.
The profiled section needs to be cut to "fit" the angle of the roof junction and if the open ends are not sealed with mortar bedded on the lead valley gutter, rain can blow back up under the tiles.
Its a clumsy looking detail but it has been shown to work.
The junction between the dormer and roof is usually smaller and more fiddly to detail than a large gable roof abutment for exemple, and I'd check here for lack of sealing and correct installtion of flashing at the abutment.
All that having been said, dinner plate circular leaks usually betray a single drip feed, not a torrent.
Limited opening up from within or an attic visit should dertermine the cause and then you need to take advice on how best to repair it.
Opening up from outside by a good roofing specialist would be your best bet because this is difficult high level work and not to be undertaken by laypersons.
FWIW
ONQ.