If you suspect that you have hyperhidrosis you should make an appointment to see you GP in the first instance. They will take a thorough history of your symptoms and medical history and might undertake some further investigations which might include blood tests to rule out the possibility of secondary hyperhidrosis.
A likely first treatment offered would be a prescription for a strong antiperspirant to apply to the affected areas at night.
The next step is often referral to a specialist. The type of medical specialist who deals with hyperhidrosis is a dermatologist, a specialist in skin conditions. In some areas of the country some services are contracted to GPs with a special interest in dermatology so you might see one of those.
Unfortunately, hyperhidrosis is regarded as a low priority and in some areas the NHS Commissioners who pay for services either limit or do not fund treatment. Even when funding is available not all the treatment options listed on this site will be available. If this is the case, or if it is your preference, you may wish to seek private consultation and treatment. You may still need a referral from your GP to a private specialist but you might be able to locate one with relevant experience near you from this link.
If it is just your feet that are affected then you could see a podiatrist who can help manage the hyperhidrosis and other problems that are often associated with persistently wet feet. You can find a podiatrist using this link.