In my experience both of you are right. There are many people who are very "desperate" for friendships, especially if they have not lived in the same place for 20+ years. On the other hand there are a bunch of people who are so much in their routines they are not open to do anything out of the ordinary. The ironic thing is that even those are often desperate for friends, they just struggle to break their routines (something you definitely must do to make friends IMO).
Which leads me to a point that is missing in the post, if you want to get to know new people, be open to new things. Just say yes if somebody asks you to go to the arcade, if you really can't but want to do something, follow up on the rain check.
>There are many people who are very "desperate" for friendships
Being desperate for friendships, in my experience, usually has the opposite effect of making people avoid you even more. Especially if you're over 30. People seem to be wired to think that "if you're a grown adult and have no friends by now, then it's probably because there's something wrong with you, and is risky for me to be the first one to take a leap of faith in you if nobody has done it so far". Usually people who already have many friends easily attract more, as it signals you're already a sociable and valuable "tribe member". Same with romantic relationships.
>Just say yes if somebody asks you to go to the arcade
That assumes there are people who ask you. If nobody asks you, then what? In my experience after I moved abroad, almost nobody asked me anywhere despite me learning the local language, making efforts to socialize, strike up conversations and exchange phone numbers. Even when I was the one initiating asking people to go places rarely end in a positive response. I think it's a cultural thing. The country I live now, people are very cold, distanced and keep to themselves, and meeting and engaging people you don't know very well is not really something wildly accepted.
Perhaps you can consider moving to a country other than the UK?
Just kidding, I've met plenty of wonderful and sociable UK people, and the joke could work (or not work, depending on what you make of my lousy humour) on almost any country.
Edit: seeing your other comment about "German speaking parts of Europe", my next guess to use in a joke would be Germany, but similarly, I've met a ton of very sociable Germans.
Which leads me to a point that is missing in the post, if you want to get to know new people, be open to new things. Just say yes if somebody asks you to go to the arcade, if you really can't but want to do something, follow up on the rain check.