You'll be after a cheap service offering both voicemail and call forwarding aka call diversion. Call Divert usually allows you to redirect your mobile calls to either your voicemail or any number. If you are setting up call diversion using your phone (this can be set up manually), you'll often be charged for the diverted calls that you receive. The charges will usually depend on which price plan you have chosen, but your free minutes will often be used wherever it is possible. The person calling will sometimes have to pay for the connection to the number they dialled, but that is all.
GiffGaff is one of the cheapest companies for mobile charges so they might be a good start for comparing click here for prices but you might want to take into account what network the majority of people you are in contact with are on if possible, if the cost after diversion per minute may depend on their network. Giffgaff is 10p to other networks and seems to be free on it's own.