Freeview is the trading name of a company (DTV Services) which is jointly owned by the BBC, ITV, Channel 4, Sky and Arqiva (who own the transmitters). That company negotiates contracts with other providers (such as UKTV, which is a commercial arm of the BBC working in partnership with an independent company) for the supply of services from channels such as Dave, Really and Yesterday (which are all part of UKTV anyway).
Saorview is Ireland's equivalent digital provider but it is wholly owned (through a subsidiary company) by Ireland's state broadcaster, RTÉ, which transmits its own signals and also negotiates contracts for the supply of services from other broadcasters. However the range of channels available in Ireland is far smaller than in the UK:
http://www.saorview.ie/channels-services/
Chris