Steve,
They supply you with their bank account details and you get your bank to transfer the money, your bank will give you option of which currency the transfer takes place in (GBP, USD or KES) and whether to the conversion is made before sending by your bank or on receipt by their bank. The bank will charge a fee depending on your bank it will be between £15 and £25 and is typically around £20.
yes its is safe, I transfer money between my UK and Kenyan banks every 2 or 3 months this way. Once you have the operator's bank details you can check online whether your bank or theirs have the best exchange rate.