There's no contradiction. Thames and gilts both pay ~5.8% on average. This is about the same as "Baa" (moderate risk) corporate debt.
https://fred.stlouisfed.org/series/BAA
Thames' debt costs are normal for a company of its type, but for a government this bond yield is danger-level high. That's why there's so much talk in financial circles now about the UK needing another IMF bailout, although I have grave doubts about whether that's actually possible given the sheer size of the UK's debt load compared to the smaller third world countries that normally need IMF help, and the near simultaneous talk in France of a bailout there too. The IMF just doesn't have the resources for even one bailout of that size, let alone two.
Don't pay attention to credit ratings of countries vs companies. They aren't comparable due to political interference and general crapitude at the ratings agencies (remember they rated sub-prime mortgage debt as AAA). They also disagree, S&P rates Thames' class A bonds as Caa3. What really matters is the yield. That's the ground truth.
Note that Thames' interest costs have been all over the place. 5.8% is the current amount it's paying, but the actual bonds it has issued have had a wide range of yields.
The reason it's considered high for a government is because government debt should be much lower risk than a company. Governments can order banks to transfer everyone's savings to themselves, they can print money, they can prevent their citizens from leaving and seize all the assets... they can do things to raise money that would be considered incredibly evil and criminal if companies tried. And of course they can in principle set bond yields to whatever level they like by making the central bank or other financial institutions legally required to buy their debt.
That's why economics textbooks teach that government bonds are the lowest risk possible and so should have yields far below corporate debt.
In reality:
1. Governments can default on their debts just like companies do. History is full of such examples. Bond yields reflect that fact.
2. Governments can sell bonds that are inflation linked, so printing money isn't a way to escape those debts. The UK has an abnormally high amount of such debt that's inflation linked. The only way to pay them back is via cutting spending or increasing tax revenue, but the UK can't do the latter (recent tax rises have failed to come close to expected revenue increases) and can't do the former either because...
3. Governments can be prevented from paying their debts by law. Some countries have "debt brakes" or "debt ceilings" that can block the issuance of new debt to pay old debt, and in other cases (like the UK) the government may rely on ideologically extreme MPs who refuse to pass laws that bring spending in line with revenues.
So you add these things together and something that could in principle be a sure bet ends up looking as risky as an ordinary company.