To provide more detail on why this project is important and what went wrong.
Firstly, forget journey times, despite what the Daily Mail thinks it's not all about "saving you 15 minutes to London" (a figure that is bogus anyway). It's about capacity. The West Coast Main Line is the most congested mixed traffic railway in Europe. Look up peak time ticket prices between Manchester and London (keep an Aspirin handy, you'll need it). Why are prices so extortionate? Because capacity is so limited that the government ordered the operators to price off demand. HS2 would have increased capacity into Euston threefold.
Stopping commuter trains (London Overground) would have gone from 3,900 seats per hour to 6,500. Regional trains (London North Western/West Midlands) from 1,600 to 6,800. Intercity trains (Avanti) from 5,800 to 21,600. That's a huge boost in capacity, which means that prices can drop (supply and demand). Paths would also become available for the container trains that run between ports in Essex and the distribution centres in the Midlands, taking lorries off of the roads.
Now let's take a look at journey times, because they do matter, but not in the way that the Telegraph would have you think. At the moment it takes 4:30 to get from London to Glasgow. So people fly because even with getting to the airport and going through security it's quicker. HS2 would have reduced London to Glasgow times to 3:40. Suddenly rail is able to compete properly with the airlines and poach passengers from the polluters. It worked for Eurostar: https://www.airlineratings.com/news/trains-versus-plane-eurostar-almost-halved-airline-demand/
"But I don't want to go to London" you may say, "how would I benefit?". Some of you want to travel from Liverpool to Manchester (and beyond). Northern Powerhouse Rail was George Osborne's scheme to sort out the appalling east-west transport links in the North. NPR trains were going to run on HS2 infrastructure between Manchester Airport and Manchester Piccadilly. They can't now, that's just been cancelled.
Some posters on this thread want better links between Sheffield and Manchester. At the moment they have to be threaded through Stockport which is far too congested to allow any improvements. HS2 would have freed up capacity through Stockport.
Maybe you want to travel between Birmingham and Leeds/York/Newcastle. Currently you have to spend two to three hours wedged into someone's armpit outside the toilet on a four coach Crosscountry Voyager (particularly now that the government have just cut the fleet). With HS2 you would have had three trains per hour, eight coaches long, and shaved an hour off of your journey time.
So why did costs become far greater than any European railway? Well they always were going to be a little higher, we are the most densely-populated large country in Europe. That we left things so late didn't help either. But why did they increase? Well when the French build a high speed railway, they don't have years of consultations and parliamentary inquiries. They get on and build it with the legal minimum of fuss. They certainly don't go building loads of extra tunnels just because the True Blue seats in the Chilterns are unhappy at having their view spoiled.
Not that views were going to be spoiled by much in the long run. Building sites aren't fun to live besides, but once the line is running and the vegetation has regrown you will barely notice it. Unlike the M40.
Then there's the usual government mismanagement. The boss of HS1 (on time, on budget) applied for the job. He was turned down (too inexperienced apparently). As a PP said, it's a really daft thing to announce what your budget is, it encourages contractors to take the piss. Keep it under wraps and keep them guessing, it forces them to be more competitive. The endless government reviews and delays have driven up costs too. What we really could do with is a rolling programme of infrastructure improvements. Then construction firms can invest in building an experienced workforce. Instead the government keeps turning the tap on and off, meaning that it covers the cost of training everyone from scratch and then watches them all piss off elsewhere because there's no more work for them.