@Geographer, after the 2016 election I felt outraged for the umpteen millionth time about the fact that because my mother, a U.K. citizen (who in fact grew up largely in the U.K.) was born outside the U.K., I -- who was born and have grown up in the U.S. where my mother now lives -- did not qualify for U.K. citizenship.
I went online and discovered that since the last time I had felt outraged, it was now possible to enter information (about parents and grandparents and such) into U.K. immigration attorneys' (or maybe solicitors, see, I really am American...) websites to learn whether one did or did not have a plausible claim to citizenship. I used
https://www.sableinternational.com/ and was advised I ... didn't. So I set that aside and forgot about it.
In late 2017 or early 2018, I got an email from that same firm advising me that a recent U.K. Court case had changed the rules and I was now a good candidate for citizenship.
What happened was that a case known as the Roumein case brought to the attention of the U.K. system not only that it was sexist that children of British fathers born outside the U.K. to British parents (born inside the U.K.), but not children of British mothers similarly situated qualified for citizenship, but that this was not OK. Also, although generally people claiming U.K. citizenship on the basis of their grandparents must claim before they are adult, the Roumein case provided (effectively) an extension to people (like me) who qualified under the new rules the case established but who hadn't qualified (because those rules weren't in place) before we turned 18.
I got U.K. citizenship. It was very easy and not particularly expensive (80 pounds, plus assorted mailing costs that probably doubled that amount). It wasn't particularly speedy (but it wasn't horrifically slow, either). I was able to apply online (I did have to mail physical documents, and show up in person at a consulate once it was determined that I could register as a U.K. citizen).
That's surely way more info. than you want, but a key point, I think, is that if the Scottish grandmother you mention is paternal rather than maternal, and you're an adult, then I don't think you can claim U.K. citizenship anymore. I may be wrong, and the website I link above would be a simple and free way to check (as would others -- I have no connection to any of them beyond having used that one, though I will say I had several email exchanges with someone who worked there and she was very, very helpful).
HTH.