In its first update on the scheme, the Bank confirmed that as of the end of Wednesday, it has bought £507m of company bonds since the £10bn programme started on 27 September.
The Bank's 18-month scheme will see it purchase bonds - effectively interest-bearing IOUs - from firms making a "material contribution" to the British economy.
Technology giant Apple, tobacco giants British American Tobacco and Imperial Brands and the US fast food chain McDonald's are among the more controversial firms on the list of eligible companies.
Apple and McDonald's have both attracted attention over their tax arrangements.
Their bonds are on a list of £110bn of eligible corporate debt, which also includes industrial and utility companies such as Rolls-Royce and Severn Trent as well as retailers Next and Marks & Spencer.
The Bank said it hopes that by buying corporate bonds, it will lower the cost of borrowing for companies as it drives down the return or yield on the bonds.
The Bank unveiled the scheme in August as it cut interest rates to 0.25% and unleashed an emergency package to ward off recession in the aftermath of the Brexit vote.
It also fired up the printing presses once more to launch another £60 billion of quantitative easing (QE), taking the total to £435 billion, and a term funding scheme worth up to £100bn to encourage banks to lend to households and businesses.
The Bank's latest update confirmed that £70m of loans have been made so far under the term funding scheme, while it has bought £392bn of gilts so far under QE.
The Bank's policymakers have repeatedly signalled that a further rate cut is likely by the end of the year, with the move widely expected in November .
But recent data showing signs of a resilient economy since the Brexit vote have begun to cast doubt over further action so soon.
Prime Minister Theresa May also took aim at the Bank's measures to shore up the economy since the financial crisis in a speech on Wednesday, saying QE and record low rates have had "bad side effects".
Mrs May said people with assets had "got richer" while those without had suffered and savers had been left "poorer", and said a shift instead towards government policy to drive growth was needed.