I can’t speak to the process and costs of diagnosis in the UK. However, I do want to encourage you to keep pursuing it if you feel strongly that you may have ADHD. The first GP you discussed it with obviously has limited and antiquated notions about what ADHD in adults is like.
Maybe take an online self-test and print and take the results to your GP to help facilitate the conversation:
ADDitude Community Moderator, Parenting ADHD Trainer & Author, Mom to teen w/ ADHD, LDs, and autism