Is it possible to do a PHD in UK by correspondence? or is there any flexible system that would allow me to do a PHD and on the same time work abroad?

I've never heard of any 'correspondance' PhD courses in the UK - the US seems to have the monopoly in that area.
It is possible to do a part-time PhD and work abroad, and visit your supervisor a few times a year.

Thank you very much for the information.
Please, does any body know about any universities which provide part time PHD in the development studies sector.

Might be worth looking at the Open University (UK) for more flexible distance PhDs. http://www.open.ac.uk