The 10-year gap equals the 2-year gap plus the difference in the slope from 2 years to 10. The 2-year gap mostly tracks what markets expect central banks to do. What is left at the long end is the extra the UK pays to borrow for longer.
Above what the Bank is expected to do
10-year gilt par yield minus the 10-year sterling OIS par yield, both from Bank of England curves. OIS at 10 years is only published from the point the Bank judged that market deep enough, around the end of 2021. This gap is the gilt's extra yield over the swap: the public finances, dealer balance sheets, and how many gilts are being issued and sold. It is not a credit spread, and it is not the whole term premium — the swap curve has a term premium of its own. The pieces inside the gilt yield are on what makes up the price.
Inflation compensation, kept separate
This is not part of the arithmetic above. The UK line is the Bank's 10-year implied inflation spot rate, which refers to the Retail Prices Index. The US line is the 10-year Treasury yield minus the 10-year TIPS yield, which refers to CPI. They are not interchangeable, so the chart does not subtract them.