Mrs May, who started her professional life at the bank in 1977, will stress the value of an open financial system which has the right level of regulation.
Speaking at a conference to mark the anniversary, the PM will say: “A free market economy, operating under the right rules and regulations, is the greatest agent of collective human progress ever created.
“It was the new combination which led societies out of darkness and stagnation and into the light of the modern age.
“It is unquestionably the best, and indeed the only sustainable, means of increasing the living standards of everyone in a country.
“And we should never forget that raising the living standards, and protecting the jobs, of ordinary working people is the central aim of all economic policy.
“Helping each generation to live longer, fuller, more secure lives than the one which went before them.
“Not serving an abstract doctrine or an ideological concept - but serving the real interests of the British people.”
The Prime Minister is expected to insist that a balanced approach to public spending is key in ensuring that the economy operates in the interests of working people.
“That means continuing to deal with our debts, so that our economy can remain strong and we can protect people’s jobs.
“At the same time, it means investing in our vital public services, like schools and hospitals, which our successful management of the economy has made possible.
“To abandon that balanced approach with unfunded borrowing and significantly higher levels of taxation would damage our economy, threaten jobs, and hurt working people.
“Ultimately, that would mean less money for the public services we all rely on.”
The speech is also set to explore how the nature of central banking has changed over the past 30 years with its new defining characteristics being “openness and transparency”.