There are screening assessments that you can access on-line to see if you have traits associated with dyslexia. The results can help you decide whether or not to undergo a full diagnostic assessment.
Some websites offer very straight-forward and simple screening tools.
If you are an adult and suspect you may be dyslexic, sometimes your employer (especially if they are a public service or large organisation) may pay for an assessment for you. However, you can also pay privately for an assessment.
A reputable registered Psychologist or specialist teacher would normally perform the tests. It would be useful to contact the British Dyslexia Association (BDA) for local assessors.
The British Psychological Society (BPS) has a public directory of Chartered Psychologists and the Health & Care Professionals Council (HCPC) have a similar service. Dig-iT keeps a list of specialist teachers who are qualified to perform diagnostic assessments which is available on request.