In general, country names, like Japan and Scotland, are not plural nouns. However, in British English, when the name of a group of people, such as a sports team, is a singular noun, it often agrees with a plural verb. This is called a collective noun or a collective singular. Wikipedia talks about it here, and here is another question about it. Here are some ...
I've upvoted @MaulikV's answer here, because although it's quite true that most people in most contexts wouldn't distinguish between compared to and compared with, I think these charts strongly suggest that historically there was indeed a tendency to use to in contexts emphasizing similarity, and with in contexts emphasizing difference.
I think we can be ...
It is not a sentence. It is a noun phrase - the head is the noun "survivors", and it is post-modified by a participial clause "clinging to a raft".
It can be used independent in the same way that any noun phrase can be used independent, eg in answer to a question:
What does this picture show? Survivors clinging to a raft.
But it does not narrate ...
There is no governing body that dictates what is considered right or wrong usage of the English language. Much of the usage can be agree upon, but occasionally, there is disagreement.
That is the case here. Some say it's wrong; some say it's right. That's essentially what Swan is saying. Put another way, some of us could argue that those grammar books are ...
Michael Swan is being subtle.
Yes, "disinterested" is sometimes used to mean "uninterested". So you can use it this way. But some people avoid this meaning and consider it wrong.
You don't know if the person who hears you speak, or reads your writing will be a person who considers it wrong, and as a non-native speaker, you will get less forgiveness of "...
The word solution is a bit formal. Also "that I searched" is somewhat stilted, and, like solution, searched is a bit too formal.
All told, if you want to sound more natural, you would say something like this:
That's the answer I was looking for.
If you actually want to preserve the level of formality of the phrase in the question, the following would be ...
In English, you search somewhere or some place for something. The object you're trying to find goes with the preposition "for". In your sentence "solution" is what you were trying to find. Therefore the correct way to say it is
This is the solution that I searched for.
Compare with: This is the room that I searched.
According to the Merriam-Webster dictionary. one meaning of roll up is
to increase or acquire by successive accumulations.
But its hard to connect the phrase with MW's definition.
A second meaning of the verbal phrase is to reduce something (e.g., roll up the maps, roll up the papers). From Collins
If you roll up your sleeves or trouser legs, you ...
I have assessed this question with a focus on British English because your quotation is from the British Prime Minister.
I did initially think you had either misheard the word rounding, or that Prime Minister Boris Johnson from whom you were quoting had made a characteristic gaffe:
We are committed to rounding up the evil county lines drugs gangs.
The term "grand" is American slang from the early 1900s, presumably from the expression "a grand sum of money" to mean $1,000. As with most questions of etymology, we don't know who first used the phrase. The best we can do, in most cases, is to find the earliest written usage, which is around 1915 for "grand."
The usage of it is quite common (for 10 grand ...
They tool themselves up
It means "Let's arm ourselves".
"Let's get tooled up" is a common expression in the UK, particularly in TV crime series. It's sometimes used in a situation where each character will have just one weapon, but it suggests there are more than enough to go round [US: around].
Although it is also commonly used of other tools,...
I have never previously heard "tot up" used in the context of the phrase you quote. I am guessing that it might be a very colloquial usage in some region, or perhaps a writer just playing with words to make the sentence interesting. In normal usage, however, it would not sound correct, because "tot" - as you note - means to count, not to gear.
The story could be true, but I don't think it is.
==> I read this as "It is entirely possible that the story is true, however I do not think it is". The speaker is casting doubt on the story's verity, as it has not yet been decided.
The story might be true, but I don't think it is.
==> I read this as "It is possible the story has already been proven ...