musicality,
This is what you can do, at least you will leave with some dignity. Find yourself a passport then go to the IOM, London office and tell them you would like to return home voluntarily
http://www.iomlondon.org/ 08007832332 get the form, fill it in post it and you will be called for an appointment to ask what date you want to return.
Even though you have overstayed, want to go return and not interested in coming back, I do not think it's wise to turn yourself in to Police like some criminal. Take my stupid advice and it in touch with IOM, you will be able to leave with 2 pieces of luggage, its a simple process.
They fail to realise we are nothing in this world! we can disappear in a split second.