Infrastructure doesn't just mean trains and roads. I really mean schools, hospitals, GPs, houses etc. The hard infrastructure to get people around. adequate drainage, adequate water and energy supply etc is also poor but just the basic public services cannot cope with the additional demand and they haven't been growing anywhere near the pace they have needed to.
Yeah, of course, I should have mentioned those too. We're going to need a push to build more of those, but like you say, staff them too, so we need to be paying them what they're worth, or the UK folk will just not be interested in training as them. If that doesn't happen we'll need to import trained workers (or those who want to get trained), but of course, loads of our folk don't want that. They'll want it when they're in the hospital or care home though, that's for sure.
Upgrading exiting infrastructure of utilities is extremely difficult and costly in built up areas, and my field of work is actually doing that in a way which is least disruptive. Doing it out of town is a doddle by comparison, probably ~10-20% of the cost.
There's a massive push on at the minute for upgrading and adding electricity infrastructure though, my company is gearing more towards that, rather than drainage.
They can sort drainage in town's and new developments out of towns etc by having holding tanks effectively (actual tanks or holding ponds), it buys time during storms for storm water, to limit flow into the existing network. They also can do the same for foul water, using rising mains (basically pumped sewers), these also get stored in tanks, and they only allow a pumped connection onto an area of the foul network which is not at capacity. They've been doing this for at least the last 15 years (largely un-noticed by most) and every new building or rebuild has to have separate foul water and surface water systems, not like the old days where it was all combined. If you notice the green kiosks near new housing, in fenced areas they're often the pump stations for foul water, and there's a big tank nearby often in the road, a car park, or an area of land with no building on. The surface water is normally a 225-600mm pipe feeding into a long pipe in the road 3x the diameter, which basically acts as a tank, but the outlet is limited to that of a 225mm pipe, or on a hydrobrake which limits flow. When there's major storms and the big pipe/ tank gets full, the overflow kicks in, into a SUDS pond. These are are easy to see, they normally just look like empty ponds, but are designed for 1 in 100 year weather events, based on assumed climate change + an additional 20-30%. There's a suds pond on my estate, never seen any water in it, even when we've had extreme rain, and the nearby river was massively flooded. There's a pump station for the FW too, and the other estate nearby also has one. When local capacity is tight, the pumps operate at night when the network is less stressed, basically means you can use the same pipe for more volume over time. I've not worked on many new or refurb developments where they've struggled to get a local connection, worse case is usually just larger tanks on site, but there's always space.
What they end up connecting the Foul water into is often a combined system, but eventually what should happen is the percentage volume within the combined systems will be less and less surface water. With old budlings and the like there's no real way to get them onto separate systems, until they eventually need a full refurbishment, and I think now full refurbishment planning actually forces separate systems.