I have to replace an existing radiator and the valves.Do I need to bleed the complete central heating for it? Should the water supply to the boiler be shut down as well?

if you have a combi or pressurised system then you need to drain down water to below the rad you are removing eg ,if rad is upstairs then drain down top rads ,if on ground floor then all rads to be drained. if conventional system eg you have a hot water cylinder then you can form an air lock in expansion pipe and header tank in loft but you need to be a competent plumber to undertake this .it saves you draining down your whole system other than that you will need to drain down and bleed your rads

Your central heating system will have to be completely emptied for this work to be carried out. The way to drain it will depend on wether you have a vented or an unvented system. Once the work is done and the system is refilled, then yes, every radiator will have to be bled. As far as the water supply to the boiler is concerned, again, this will depend on the type of system you have installed. Either way, none of this is an issue to someone who knows what he's doing. Spyros Spyrou