No, the government buying its own debt is a very famous accounting trick designed to create more money in the economy. This act is the basis of the fractional reserve system, which in turn is the basis of all modern money.

The Federal Reserve bank buys bonds from bondholders (either newly issued bonds from the government or bonds from my safe deposit box). And in return it puts money in a bank account. Where does the money come from? It is just numbers in a database. The Fed just edits the database. Only the central government, which controls the currency, has the power to create money out of thin air in this way, but that power is very important.

(In other times, when the economy is really hot and inflation is soaring and we need to cool down, the Fed does the opposite: It raises interest rates, which causes people to want to buy bonds to get more interest, which causes people to spend their cash for those bonds. And, as each bond is bought, the Fed just erases the cash from bank accounts. The money vanishes! Remember, money is just a score in a game, the game of "keeping the economy working so that people can eat". It's not made of metal or anything. That was the old way, the way that didn't work.)

You can't get the same effect by selling bonds to England, because then England will pay for the bonds in dollars, and England can't create dollars. They have to buy dollars with pounds. So the total supply of dollars in the world would remain constant, which is not the point of this exercise.

(Now if I really understood econ we could go on to talk about why this little exercise might not work this time, about the "liquidity trap" and the "zero lower bound". But my time is up.)