The deals include 295 bilateral trade deals, 202 regulatory cooperation agreements, and hundreds of detailed agreements on fisheries, transport, customers, agriculture and nuclear fuel.
Multilateral agreements based on consensus involve 132 separate parties, the research found.
A further 110 separate agreements with the UN and World Trade Organisation have been excluded from this analysis, the Financial Times said.
"While Brexit is often cast as an affair between Brussels and London, in practice Britain’s exit will open more than 750 separate time-pressured mini-negotiations worldwide," the Financial Times said.
The need to renegotiate deals will put pressure on staff at Whitehall where, for example, only three people are currently dedicated to negotiating aviation agreements, the Financial Times said. These negotiators will need to renegotiate 17 existing agreements with third countries and around 40 bilateral deals that include EU clauses, it said.
"This may need to be done in the space of a few months, once the EU-UK terms are clear and Britain decides how much of its aviation regulation will be repatriated," the newspaper said.