ahhhh, structural engineers.
we went through this sort of bolleaux.
First one we hired, reputable well known regional firm, recommended by architects etc, charged us up front fee £1000. After months of inactivity we asked for a refund, they tried to charge a £70 admin fee. Dickhead. We got the full amount back.
Second one, huge national firm. Did an OK job for extension, pissed us about for a price for doing attic calculations. Charged us for a meeting with our architect including their travel, which amounted to bumping into one another while having lunch (I shit you not). Charging us for extended telephone calls while the engineer unburdened about his wife's medical issues as the reason for delays. Never even visited the site, not once. We refused to pay a huge invoice they couldn't justify the billable hours. The local office boss made threatening calls to me and I had to block his number. I bollocked their head office. They cancelled the erroneous invoice.
Third one - lovely firm I think our nearest office was Huddersfieldish (so furthest away) quoted us half the price of the second one for the same work including his travel. Turned up on the day, did the work, chatted to our contractor about it, gave us an invoice and joked that it was needed for building regs but money for old rope for him this kind of work. Love him.
What I'm getting at, in my usual roundabout way, is just demand the calculations. Ignore the engineer and go to their head office if they have one, or the most senior boss of his office and insist. They are yours, you've paid for them. Keep insisting. Calculations or refund NOW. His choice.