illuminator,
You have a typical lighting setup, but what LEDs you put in depend on what style you want, and how bright you want it. If you want to keep the 3-way lamp setup, then you can do this, but LED bulbs in the bayonet base are not common. LEDstuff has GU10 and MR16 halogen replacement bulbs, which go up to a 50W equivalent (
the high power 5W LED). 6 of these would be plenty of light. I would recommend the GU10 base as it runs directly from 230V and does not require a power supply like the MR16 base. If you are able to swap the fittings to GU10, that would be ideal.
Another option is to remove the 3-way light fitting and use a
downlight unit. 12W and 15W versions are available with a wide 120 degree beam angle, so they are good for general lighting. The 15W one is similar to a 100W incandescent, so two would be enough light for a medium sized lounge.