The British weather has a wonderful reputation for taking a good event and making it wet. Rather than fight it, the best approach is to cater for it. If your venue is big enough, you could have a reserve hunt which takes place purely indoors. This can be a costly option which would ram the building full of people. Plan all the outdoor clues so the participants stay on well drained paths, avoiding areas that could go muddy. If there are sheltered areas outside, put a clue there which will result in people gravitating to the dry areas. Try not to place a clue miles away from any rain respite – you will just soak absolutely everyone.
People are hardier than you think – they are already committed to take part in this event and so long as you can minimise their exposure to the dampness, they will get out there, get on with it and maybe even enjoy it.