First of off, you will need to check with your local passport office, whether it is legal or not. If they ask the reason, you can tell them it's to stamp a visa. They would understand this.
If it is legal to send, they will give you a letter or a form authorizing you to send your passport. With that letter, you can go to DHL or UPS and courier the passport to London.
If you are not a citizen of Saudi Arabia, then you have to approach your country's embassy or high commission and ask for instructions for this.