In addition to Company Law, the Premier League has its own Rules relating to club finances, accounting and good governance.
The Premier League, Football League and UEFA each has its own regulations governing club finances. The most widely known FFP policies are probably UEFA’s. These pertain to the licensing system for teams who wish to take part in European club competitions.
The Premier League has a number of financial rules in place, including requirements for clubs to pay transfer fees, salaries and tax bills on time. They must also submit accounts annually, and disclose payments made to agents. You can read these regulations in full in the Premier League Handbook, primarily Section E: Club Finances.
Outside of these obligations it is up to individual clubs, who all have their own directors and senior executives, to make decisions over how they spend their income.