Actually it's not a silly question at all. You do not have time or a place to change between events so you need something that you can do all three events in. If you've ever tried to run in cycling shorts you'll know that this is not a good idea, and cycling in running shorts or swimming trunks is a recipe for saddle sores.
The answer is basically 'triathlon gear' - people tend to either wear a tri suit, which is a skintight one-piece, or a two piece version, with shorts and a top (this means you can change the top between cycling and running if you really want). Either version will have a narrow pad to give some protection when cycling but not wide enough to impede running. The pad is also of a type that will not absorb water, so you can swim in it too.
In addition to this, if the water is cold enough, you will want to (and sometimes be required to) wear a wetsuit. These wetsuits are specific to triathlon and much thinner than other kinds of wetsuits. They are also very close fitting and can tear if you aren't careful. It helps if you are greased up a bit before you try to put it on. These range in price between about 100 quid and... a lot. They also give you additional buoyancy so they make swimming in open water somewhat easier. I would also recommend decent goggles, preferably ones with glare and UV protection.
Finally, you will need easy to take on and off bike and running shoes, and a bike helmet. Plus decent athletic sunglasses and a lightweight sunproof hat for the run. Suncream is also a must on a hot day. That's really about it.