Normally you would only pay a deposit locally, the rest should be paid to your lawyer's ESCROW account directly from the UK. More often than not, you will find that the lawyers here used US banks to hold money in to ensure that there are no delays. Once everything is checked out by the lawyer (property taxes up to date, title ownership, utility bills up to date etc.) and you have signed agreements, the lawyer will pass the money on to the owner. Depends where you're buying and what price range. Most ex-pat community housing is transacted in $USD.
Your best option would be to shop in the UK, rather than looking for a Dominican $USD / ?STG exchange rate. I used Barclays last time and for large amount they go to the trading floor.