A weak battery can cause longer starts, but so can a few things. You should record this, upload to a suitable site and link it here.

Watch your taco, if moving around at all on idle, you have issues still.

Having changed the cam belt recently on mine, really surprised they managed to put a cam belt on so badly, as to cause failure in 15 miles, (the belt supposed to last 240,0000km or 10 years), you scored death of cam belt, in less 1% of its lifespan, you would nearly have to say incompetent or did not have the tools to undertake the work. Either way, this is not something that should or could happen from a cam belt change. Did they supply the engine/repairs free, because this was always their mistake, doubt anyone could see it any other way, when the belt died, so quickly.

When I changed the cam belt, spent at least an hour admiring what the procedures don't really tell, how well the engineering on these engines is, sure it tells us the way the timing is set and maintained, but till was there didn't notice the way they don't put stress on the Woodruff key by centring the timing belt or how they have engineered the bottom crankshaft cog, it's pure poetry to me.

Who was the manufacturer of cam belt supplied, are they aware this happened, did they investigate ?

The engine itself is arguably one of the better PSA builds, serving in multiple models for Peugeot. PSA produced them for use with other name brand manufacturers, such as Land Rover / Ford.

All the procedures required are documented here.
4007 - Maintenance Schedules & General Information for Servicing | Peugeot Forums

 

In my case, it was a leak in the fuel system, causing the fuel filter to be almost completely clogged. I used Eolys 176 (recommended by the vehicle manufacturer) and a slurry-like compound was created which almost clogged the fuel filter. In addition, I was then recommended Infineum, and remember the most important thing, on some engines the fuel filter maintenance cycles have been shortened further from 60,000 km to 30,000 km or to 20,000 km.

 

some engines the fuel filter maintenance cycles have been shortened further from 60,000 km to 30,000 km or to 20,000 km.

If using the MANN WK12001 filter, I have recommended, doubt that was reduced to 20k (maybe they have been) they are fairly expensive to only last that distance and in practice calling that not correct, at least regionally here, and what I have seen from my engine, and a friends Land Rover with same engine.

Fuel filters are not all the same, and inside construction, stuff we rarely see, matters. I did 80,000'ish on my first one, and not even worried about my current one @ 115,000 km atm, I check the pressures every 20,000km or thereabouts. Given the price of Piezo Injectors through rather change fuel filters vs. have injector(s) break. So, it is what it is, and depends on your own abilities to maintain things to a degree.

One thing, I really just can't quite get my head around, is the injection rate for DPF fluid is about 15ml per tank, let's go high and say 20ml, and from what I've read fuel soluble, anyway how does that manage to block the fuel filter when it is mixed in the 50 litres of diesel, each time. Just feel like something else would have to be at play for this, maybe contaminated fuel ?

Infineum, DPF fluid

That is a good tip.