Donetsk is served by an international airport (DOK), but you aren’t likely to find any direct flights from the UK.
Austrian Airlines operate links with the UK via Vienna, or alternatively DonbassAero is the region’s airline, operating flights to Kiev, and other major European cities.
By Train
Intercity (overnight) services run from Kiev to Donetsk and take approximately 12 hours – check out the excellent Man in Seat 61.com's Ukraine page for information about a potential rail adventure!