The government agency in the United Kingdom (UK) that handles visas is called UK Visas and Immigration (UKVI), and they can be contacted about visas through their websites. For contact from within the UK, use www.gov.uk/contact-ukvi/overview; from outside the UK, use www.gov.uk/contact-ukvi-outside-uk.
For contact from within the UK, as of 2015, the UKVI website directs visitors to regular mail addresses, email addresses, contact forms and links. That website also provides telephone numbers, but there is an added fee when contact is made by telephone, according to the UKVI website.
UK residents may also be eligible to use one of UKVI's seven premium service centers where it's possible to get same day service on visa needs. There are significant fees for using the premium service centers. Non-UK residents may also be eligible to use the "super premium mobile service" if they are inside the UK at that time. The super premium mobile service sends a UKVI courier to the person's location to collect any needed information. This super premium mobile service is expensive.
For non-UK residents, the appropriate website supplies mail addresses, email addresses, contact forms and links. If there is an urgent need, as of 2015, to contact the UKVI from outside the UK, telephone and webchat facilities can be used, but there are additional fees for those services.