Also bearing in mind that it is not just the immersion in water for prolonged periods that kills you.
Cold Water Shock is when you fall in the water and the cold water temperature makes you gasp as you are immersed. This means you swallow a shed load of water which often enters the lungs causing primary drowning, but can also cause secondary drowning as the salt water causes your lungs to produce fluid that can cause death if not treated.
If someone falls in and you pull them out and they seem fine, you should advise them to go to A and E for a check up....Just in Case.
As Alan states, Self Inflating Lifejackets are relatively inexpensive and considerably less bulky than they were in the past. I am sure that the RNLI do free safety checks on them for you also!