No-one has a full 360 degree radar but the RN (2 flights) and the RAF (6 flights) have a radar with the scanner mounted behind the MRGB on the spine which gives a 330 degree view (15 degrees blind arc either side of the nose).
So the answer is that 2/3 of the land-based UK SAR assets use a full sweep radar instead of a weather radar with (I think) a 60 degree sweep pointing forwards that the others have.
Not only does the Sea King radar give an all round picture but it was actually designed for maritime use and has a minimum radar range of 75m - this allows the aircraft to close with vessels/cliffs etc in almost zero visibility and means you can keep the aircraft pointing into wind as you manoeuvre, having let down to the hover.
The all round picture means that you always turn into an area that has been cleared by radar although the blind arc on the nose means regular clearing turns if you are operating below 1000' over the sea.
A full 360 radar would be the best solution but would be difficult to achieve without extra scanners and increased complexity/weight unless you use a mast mounted radar which would have a huge blank area in the aircraft shadow or un underbelly mounting which would limit ground clearance for landing on uneven ground.