I really appreciate your detailed reply. Based on your information we took some further actions/tests.
First we downgraded the firmware to the latest version recommended on the UK web page. Although as I mentioned already, the 1.02 version was installed by the the technical support of the retailer we bought the router. I wouldn't expect that they had to consider every small detail about any router model, but it seems like a loose job to install a not recommended firmware (which after all hasn't solved anything of the former issues).
The time issue has not been fixed after the downgrade though. Anyway, if I recall it correctly the current 1.01 version was installed, when we first bought the router and the time problem was there.
However, we noticed something, which actually explains the bizarre behavior of the wrong time indication. With NTP enabled, and both when DST is enabled or not, the current router time will show the
inactive date and time settings of the manually settings fields, which when is offset, the router current time will be wrong, too. It seems that when I login into the router's settings page, the router current time will be synchronized with manual settings no matter if the NTP is enabled. It just ignores it for some reason. The thing is that if I disable NTP in order to be able to edit the manual settings and press the button to synchronize the time with computer's time (the correct current one), then reenable the NTP and reboot the router, when I login back after the reboot, the (deactivated) manual settings are wrong again (the router current time is synchronized with them, so also wrong). Although the wrong manual settings indications keep track of the previously wrong time (which cannot figure out from where is defined) and is not some random wrong one. I hope I haven't confused you with my description.
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Therefore, I assume the possibility that in your case the router current time indication is correct because, even if you don't have them activated, your manual settings are correct. It is then worth the test to set them wrong on purpose enable back NTP, and if they'll be kept wrong after rebooting, to check if your router current time is now wrong and synchronized to the wrong (anymore) values of your manual settings. Could you please try this, if possible?
Any speculations on why NTP is ignored, at least when we login into the router's web page, despite if the manual settings are deactivated and NTP enabled, or where does the (wrong) manual settings time is provided from, since it is not for sure informed from the (correct) computer's time after rebooting the router.
Note: When I changed the NTP server (from the one you use) to time.euro.apple.com the manual settings values changed (though into wrong ones again), I tried different time zones without any effect, but when changed again the NTP server into the ntp.dlink.com, the manual settings haven't changed as well (like before, when I changed from ntp.dlink.com to time.euro.apple.com). Every time I reboot I have NTP enabled.