You can arrange your overseas mortgage either through a UK bank or an international lender.
One option is by re-mortgaging your UK home to buy the overseas property outright.
Whether you should (and can) do this will depend on, your own personal circumstances. Do you have a large equity to use, how good is your credit rating and what are the UK interest rates at the time you apply.
Alternatively you could borrow from a UK bank to buy the overseas property, using a UK bank operating in the international market and in the country you are buying in.
Some countries may be easier to obtain a mortgage in, for example in traditional countries like Spain, Italy or France than the North Pole or some obscure island retreat.
Arranging the mortgage abroad
You could look at using an overseas lender probably via a specialist international mortgage broker. Interest rates in some countries are far lower than in the UK, so you might be better off by borrowing abroad in those countries.
Also consider any impact of borrowing in a foreign currency on you in your local currency terms being the pound sterling, unless you are moving abroad fully to that country.
What about the deposit
The deposits for properties overseas can be as high as 40% and in some cases non-refundable, so be careful you have secured the property with full legal title before handing over your hard earned dosh.