Hmm! Some taps today are sold as high or low pressure. Meaning I suppose, those that work off a low pressure supply and those that work off a high pressure supply. If as you say you have just had a new boiler in and the hot water is off the high pressure supply, one assumes you have had a combi boiler fitted?
What that basically means is that the hot and cold tap now both share a common high pressure supply so the hot will affect the cold. You can check it yourself. Turn the hot water on and watch the speed it comes out the tap, then turn the cold on and see if the hot water runs slower. You have then established a link between the two taps.
All this high and low pressure tap stuff is relatively modern, I suppose because we import so much now days from countries that use different water systems than we do now. Most of our cold and hot supplies because of the wide spread use of combi boilers now come off the water main supply, which is usually regarded as high pressure as opposed to a gravity supply from a storage cistern which is usually regarded as low pressure.
And of course price, a low pressure product is probably made to a lower standard than high pressure so cheaper to make.
As has already been said, when you first turn off a tap a certain amount of water is held by the vacuum made behind the moving column of water in the spout and this takes a while to stop dripping.
The basic thing is though, if you turn a screw down tap off and it is working properly it should not keep dripping unless there is a further problem. The lads are saying it might be the seating and that may very well be the cause.
But there are a few types of same size tap washer and some are made of different materials, some designed for different makes of tap, some designed for different temperatures and possibly pressures and some the amount of torque a person applies to the tap. So are they the right washers for the taps you have?
Also the fact that when you turn the hot tap on it affects the dripping cold might mean the tap cannot hold the static water pressure of the main to close properly, but it can close when the reduced dynamic pressure is applied. But in theory if that where so, then once the hot tap was turned off the cold should start to drip again. Does it?
Basically ceramic disc taps ae okay but they can drip as well if any dirt gets onto the disc faces or they become worn for some reason.
As said though, to be sure I would take the easy and possibly cheapest option first and check the washer type then re-cut the seating if it is required. You could then Google your tap type and make and find out what pressure the tap is designed to take.
Normally though like somebody has said about re-washering, I have re-washered so many taps over the years I can't count them and very rarely been required to reseat a tap. Also usually a standard good quality vulcanised 1/2" flat tap washer has been sufficient for a standard screw down tap. But washers on taps can get complicated and we have not even spoken about the variety of jumpers or special washers you can get yet
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