If you put down a 30% deposit, you don't have to prove your income for a Florida mortgage.

It takes about a year or two years or so to get a US credit rating.

You can re-mortgage a house in the UK to purchase a Florida property outright but you'll lose the UK property if you don't keep up the payments on the mortgage.

Most people applying for US visas sell their UK property to raise the equity for a US home purchase and then take out a US mortgage if this isn't enough for an outright purchase. You will not get US resident rates for a mortgage until you have a proper credit rating so will pay 'alien' mortgage rates which are around 1 - 2% more than the US resident rates.