The only way that ADHD can be diagnosed is via the medical route (such as a psychiatrist or clinical psychologist). It's not something that an educational psychologist or specialist teacher can do. I can highly recommend clinical child pscyhologist Dr Selina Warlow and further information can be found here: https://www.drselinawarlow.co.uk/
If you think that your child has ADHD, the first step is to talk to the school as there must be clinically significant evidence in at least two settings for a referral to be considered. I regularly write referral letters that bring together information from screening forms completed by the family and school, background information, my observations in the assessment and the child's own perspective and these letters can be shared with the school. It is important to note that there's more than one type of ADHD and symptoms can go under the radar such as the inattentive type (that used to be called ADD) with symptoms like zoning out, being easily distracted and procrastinating. However, I'm coming across increasing numbers of children and adults who appear to have undetected difficulties with language (such as not understanding what others are saying) and therefore appearing to be daydreamy, etc. may be more linked to language than ADHD.
For those age 16+, I can formally assess and conclude that someone has a profile which 'strongly suggests' ADHD. This is not a diagnosis but it's enough for university students to use my reports on the basis of probable ADHD and apply for the Disabled Students' Allowance. I undertook ADHD training with UKAAN at the Institue of Psychiatry, Psychology and Neuroscience in London as well as with one of my professional bodies, Patoss. However, I still write referral letters for adults that can be shared with the GP to seek a formal diagnosis.
Please contact me if you'd like details of private assessment centres / professionals who can medically assess for ADHD in children and adults.