It's not the depth alongside, a consistent 2m scoured by the strong ebb in the Run which can reach 6 knots, but lack of it over the Bar which dries to 0.4m MLWS and changes with meteorological conditions and flood, or drought, upriver.
The tides are complex, with double HW producing a virtual stand for 3-4 hours. I've rallied up to the friendly sailing club in Christchurch, and dragged my keel all the way back - it really is a very shallow harbour! - but never stopped at Haven (Mudeford) Quay where berthing is restricted to fishing boats. To access I advise mooring a few yards further in where there's a 3m pool out of the tide from which you could dinghy across to the solitary pub which does good grub - but the beer is cheaper in Highcliffe Sailing Club next door!
I presume you mean Mudeford quay as in Christchurch Harbour entrance. 1.6 is a lot for christchurch. The bar is not much below chart datum but varies each year. Plus we were about 0.25 low with the pressure at the weekend.
once at the quay there least 2m at low water but not much protection depending on the wind direction.