1) The astronomical twilight is pretty close to actual Fajr, but it can be off several minutes (sometimes more than 10 minutes). Once I checked it in Iran and on average it was about 5-7 minutes earlier than the official Adhan there.
Islamically, the time of Fajr must be discernible by the naked eye. If in the UK astronomical twilight is discernible (by going to a nearby area that has less light to verify), then yes that would qualify as Fajr. Otherwise, as a precaution, you’d have to wait until you are certain Fajr set in.
So if you can check in surrounding areas that are darker that would be great. Otherwise you’d have to wait a little longer to be sure 100% that fajr set in.
2) According to his fatwa, if the sun does not set at all, then for prayer one has to refer to the timing of the closest location that does have a night. And for fasting, he says one must travel to another place to observe the fast, and if he cannot then travel later to do the Qadhaa.
Now if the sun does set, say for 2-3 hours, but the sky doesn’t become dark, then whenever the sky starts to brighten up that’s the beginning Fajr