OK Your Slackness ............... the pukka job first. This is what I would do...
Assuming the existing deck is still sound ........ fix 4x2 timber joists on top of what's there. Infill between the rafters with 100mm (4") Celotex of Kingspan insulation. Cover with 18mm shuttering ply. Finish with traditional "built-up" felt.
Built-up felt can be perfectly good if done properly. I use flat-roofers whose jobs have been known to last 25 years.
They use traditional hot pitch, but modern felt is fibreglass based, and a million miles away from the old bitumen felt.
You'll need new (much deeper) fascia boards now. (Not the most attractive thing, but well worth it.)
Use uPVC for the fascia boards ...... white, brown, or black..... or paint them.
Result: new roof covering and fantastic insulation.
If none of this possible, or too expensive, then just let them rip off the old felt. The deck may need replacing as well. Re-felt using the felt I mentioned above.
There are so many bandits who profess to do flat roofing, use only established companies. It possible, get a reccomendation.
Ask at a local Builders Merchants for names.......... or ask a friendly architect.
Virtually anyone can join "Trade Associations" for a fee. Don't necessarily rely on them.