Firms like mine do your extensions on your behalf, as most of our clients file after the due date.
US - has a Jan - Dec tax year. For calendar year 2005, taxes are due Apr 15 2006. Your return is due Jun 15 2006 (assuming you live abroad), extensions available through Aug 15 2006, 2nd extensions through Oct 15 2006, and final extensions through Dec 15 2006.
UK - has an Apr - Apr tax year. For year-end Apr 2005, taxes are due 31 Jan 2006. Forms can be filed any time prior to then. No extensions available, but if you don't owe money, a late return has fewer consequences than late returns with balances due.
I am sure many people will post firms they like. If nobody posts any recommendations, feel free to contact me. You should shop around and find someone you like working with.
Generally, the time to hire the accountant is before you engage in a taxable transaction (such as cashing out a retirement plan or selling a house) rather than after. The number of options to reduce your taxes beforehand are always more than the number of options remaining after a course of action has been set.
Have a good tax time,