You are confused by the fact that the UK tests far more than any other country, so their case numbers are higher.
it is common for Covid Deniers or anti-vaccine types to point to a specific country as “proof” of their contentions, and since most don’t last very long here, by the time country’s situation changes, they are gone, and don’t have to explain why their proof evaporated. Two months ago, the Antivaxxers were using Chile as proof that vaccines don’t work. Now Chile has less than 1,000 new cases a day. Then, it was Israel as proof that vaccines don’t work, but Israel has less than 1,000 cases a day.
In most countries, increasing vaccination decreases new infections.