In the USA TV programmes are often made specifically for sponsors. (i.e. the sponsoring company have the initial ideas and then pay for them to be developed). The term 'TV soap' was introduced into our language through the serials shown in the USA to promote the products of soap manufacturers.
Until fairly recently (1991), sponsorship of TV programmes was completely prohibited in the UK. (Even now, sponsorship is only permitted of particular programmes, not of entire channels). There are strict rules, which you can read in this Word document from the regulator, Ofcom:
http://www.ofcom.org.uk/tv/ifi/codes/legacy/co de_prog_sponsor/itc_code_prog_sponsorship.doc
Theoretically UK programmes are sponsored in the way that your post suggests. i.e. the sponsor contributes towards the production costs. However many 'sponsored' programmes (e.g. on Dave) are repeats. In such cases the sponsorship funding is paid to the station which transmits the programme (to help fund their purchase of the broadcasting rights), rather than to the production company which made the programme.
Chris