As long as the tread depth is above 1.6mm across 3/4 of the tyre then it's not an issue, regardless of what the tyre police on this and other forums say.
Many suggest replacing them at 3mm but personally If 1.6mm is legal then there is no reason not to run them down to 1.6mm. Even Michelin have said that this is pointless and that tyres would be worn down to 1.6mm.
There are reasons to avoid running tyres down to 1.6 mm wait until it is raining with pooling of water!
As the the tread depth diminishes, the tyre loses capacity to clear water, the 1.6mm tyre will be prone to aquaplane over the tarmac surface, steering control and braking capacity will be diminished or even lost altogether. The UK limit of 1.6mm is probably too close for comfort, I believe other countries enforce greater depths for minimum tread, there is no excuse to skimping on tyres, they actually a bargain for the important function they perform. What do you save anyway? Four set of tyres in 10 years, or 5 sets in 10 years of motoring, That is a difference of only £20 / annum, barely worth the bother