What is the cheapest brand of printer to buy with regards to ongoing
costs.  i.e. Which manufacturer sells the cheapest cartridges ?  I
live in the UK and am interested in a UK cost comparison only please..

I did a calculation for this some time ago; I can not locate it now,
however, I remember the results. It was non-UK, however; also, several
months have passed and the price of the cartridges may have changed.
If you use original manufacturer cartridges, the lowest cost per page
printed is with Samsung laser printers; if you use compatible
non-original cartridges, lowest cost per page printed is with HP laser
printers (you have to choose a HP laser printer for which non-original
cartridges are available, however; they tend not to  be available
immediately for recently released products).

I hope somebody else can provide you with more detailed and relevant information.