Craig, first off, finding this place probably wasn’t a bad start. Don’t overlook “Driver Vacancies (Members Only)”.
My general advice is - be the difference. There are likely to be many drivers (new and otherwise) looking for work in the same companies that I imagine you’ve approached (or should have done!). The only likely advantage you’ll ever create for yourself is establishing a first impression, and if you’ll excuse the cliché, impressions are lasting.
Finding a job in any given profession in the current climate, very much an employer’s market, means that you have to demonstrate being able to add value to an employer. As a new driver with previous experience in fitting HGV tyres - you’re mould-able to any given employer which is something that some of my clients stress as highly desirable and you have a skill from your previous experience which they can utilise. You should be able to stress both of these points.
When it comes to insurance purposes, what you’re being told is true. Infact, you wouldn’t even be covered if you have an accident in a 7.5tonner. I have no idea why agencies think this is a viable solution, and I work for one! Firms can however have their underwriters negotiate clauses in cases such as your own - they’ll only bother if they think you’ll be worth the risk however. Perhaps you could negotiate a lower starting salary with a review after say 12 weeks. Or you’ll pay towards an excess in the event of an accident to which you’re liable. Make it as difficult as possible for them to find a reason to reject you.
Your previous experience should give you approachable companies, or at least names of key decision makers that could make a difference in finding you a job or not. If you don’t know who they are - speak to the people that you used to deal with, ask them for the best contacts, more often than not - there’s more than one. If you’re planning on writing an introduction letter / CV (which you should), personalise it to each and every transport manager / HR officer. Use their websites to extract as much information as possible and pick up on the ‘tone’ of the company.
Most small, family firms will want you to ‘fit in’, which is probably more important than your actual ability. Skill can be taught, personality & attitude can’t.
Expanding companies will want reliability - they’re also likely to invest in things like your HIAB / ADR if you’re going to be in it long term.
Established organisations are likely to want a professional approach - doesn’t mean you can’t add some personality to it though.
Hope this helped!