Pekka,
Your right about the Congers going offshore to breed, but that occurs during may/june so the big eels have already returned inshore.
My advice (for what its worth) is to avoid shooting one at all costs, I say this for a number reasons....
1) They are extremely powerful and it would not take much for them to do some serious damage when shot with a spear.
2) Like all eels they are difficult to kill cleanly due to the muscular content of their body, i.e. even if they are brain dead then the blood still runs through muscles, this spasm effect will make them appear to be alive for much longer, the result being that they can still cause alot of damage.
3) They generally live in very small holes/caves etc with only their head sticking out, the rest of the 5-9ft of the eel (depending how big it is) will be out of reach, therefore even if you do shoot one, I doubt any man would have the stength to haul it out of its hole. (its very rare to see one free swimming, unlike the moray eel)
I'm sorry to put a downer on your thread, but I would hate to see a fellow spearo get hurt in his quest for a big fish.....
Good luck, and stay safe, even though you are in UK waters there are still some fish that can cause some damage if upset.......