Travellers to Ukraine need to arrange comprehensive travel insurance before visiting the country, because there is only provision for basic healthcare for travellers from the UK to the country.
Hospital standards away from the main cities can be very poor, and visitors should consider carrying a sterile medical kit including suture needles, syringes and dressings with them as there are often shortages in local hospitals. Most doctors will not speak English, although you can get a list of English Speaking doctors from the British Embassy.
It's a good idea to stick to bottled water outside the main towns, and you may want to consult a doctor prior to visiting Ukraine in order to check whether you need any inoculations.
Tuberculosis, Diptheria hepatitis, and tick borne encephalitis are all problems in Ukraine, and HIV is at epidemic proportions. You should take all precautions necessary prior to travel and whilst in the country.