I am visiting Florida from UK on an ESTA and have mistakenly booked return flights 92 days after arrival.
Is there an easy trip to make to a nearby country which will allow me back to Florida and stay till the 92 days and catch these flights?
Unfortunately you made a pretty bad mistake. Firstly you'll have to go at least as far as Guatemala to restore the clock, and secondly when returning to the US so soon after such a long visit (even if only to catch a connecting flight home) the immigration officers will highly likely assume you're trying to live in the US. And if they make that assumption, it is fully up to you to convince them otherwise, which will be hard.
Have your boarding pass/flight confirmation back home+documentation proving ties to the UK ready for this, and even then there is no guarantee. Once deemed inadmissible, you'll never get in visa-free again.
If at all possible, I would seriously re-book the flight home.
Another option would be getting a B2 visa, which usually allows for multiple entries within 10 years, with a 6-month leave being given on each entry. However, be warned that, although a granted visa would solve the problem, you will be placed under closer scrutiny by the embassy than by the CBP if travelling visa-free, and if you're ever denied a visa, you can never enter visa-free again and will have a harder time obtaining a visa in the future.
As pointed out by Dorothy, in all likelihood it'll be cheapest and easiest to just modify your ticket.