As soon as you enter british water without permission then you are breaking the law.
Therefore you are an ilegal immigrant.
No you’re not Jeff. If you aren’t coming from the EU then you have to fly a Q flag (look it up) on entering our waters, otherwise you simply have to contact the relevant authorities on arrival, much like getting off an aircraft.
Here are the instructions to those operating pleasure-craft which most of these boats are:
“Anyone on board who is not a UK or EU national must get a UKBA officer’s permission to enter the UK from a place other than the Isle of Man, or the Channel Islands. As the person responsible, you must make sure that anyone requiring immigration clearance (including yourself if appropriate) obtains the necessary permission to enter.
If there is anyone on board requiring immigration clearance, they’ll need to contact the nearest UKBA office by phone to arrange clearance. The National Yachtline will be able to advise on how to do this.“
So Jeff, they’re not breaking a law until they fail to notify a Border Agency official of their arrival.
You’ll probably keep on about turning them back though Jeff, but they’re not illegals at that point.