Although you might find a UK company which will act as agent for a Barbados financial institution (and probably charge you heftily for doing so), it's extremely unlikely that any UK firm would offer a mortgage on a property in Barbados. This is because any lender needs to know that, if you fail to keep up the repayments, they can easily take possession of the property. (It's unlikely that any UK firm would want to try taking civil action through the Barbados courts).
It might possibly be worth asking at a larger branch of Barclays Bank to see if they could assist you with arranging a mortgage through First Caribbean International Bank (which is part of the Barclays group) but it would probably be simpler to deal directly with FCIB:
http://www.firstcaribbeanbank.com/
Remember though, non-residents purchasing properties in Barbados have to put down a deposit of at least 40% and the maximum mortgage term is only 15 years:
http://www.homesgofast.com/caribbean/BuyinginB arbados-Theguide.php
Chris