I might even be able to solve there problem in that first hour, or at least provide some answers.
That sentence has all the alarm bells ringing for me (and it's not just the grammatical error).
If someone is asking you to complete some consultancy because they have a known 'problem' (your word!) and it can be 'solved' in a 1 hour session, then I suggest an hour's chat with a suitably qualified and experienced coach would yield greater benefit (cost £500-£1200 depending on the coach) - it is 'self-solveable', they just need the facilitated route.
If it is genuine consultancy, you would measure it in days and again, a suitable consultant with appropraite qualifications and experience would be in the region of £2,000 - £4000 per day.
If they do not have the appropriate qualifications, experience and track record, I'm not sure they would add any value - even the £30 you mention.
So .... I would advise that you progress with extreme caution and open yourself to critical challenge. From the very limited information on view, I'm not sure payment would be an issue: getting the job would.
You could always do 'pay by results' on an agreed scale. We've offered this many times - pay nothing if the intervention achieves nothing and a sliding scale for success. No-one has ever taken us up on it as a small percentage for achievement can become a huge charge - most want to play safe and spend a few thousand.
However - maybe worth considering?