HS2 will happen. Every party is for it (not even Corbyn would want to stop it) so it's just the usual slow process of getting everything into place.
The money isn't coming from a bit pot that would otherwise be used for something else. If it gets built, the finance will be raised. If not, there's no bank account with a few billion that can go upgrade other lines.
Every five year period has a budget, and many projects are already planned for this one and the next - but as you probably know, things have slipped on the various electrification projects. It's VERY costly to do work on a live railway, and even if existing lines were upgraded, adding new platforms, new tracks, all new signalling, newer overhead lines to cope with faster trains would mean a shed load of bother, and still loads of compulsory purchasing (so the NIMBYs would soon be out to stop that happening too).
I don't see any reason why things should go over budget, besides a few influential people in the Chilterns succeeding in getting more of the line put in tunnels, at huge cost. Why, I do not know. Since when was a two line railway considered an eye sore, compared to, say, a motorway?
Clearly the existing lines need upgrading too, and that will happen. People along the west coast main line will suddenly be able to get more services and will benefit greatly, and more freight will free motorways to make driving more congestion free. But eventually these new lines will fill up, and that's why someone needs to look longer term at HS3, HS4 etc.
We need a modern railway, not upgrading 100+ year old tracks that weave all over because it was easier than cutting through. Wider, faster, greener trains - with decent connectivity for rail passengers who will want to be connected throughout seamlessly.
I'd say that if anyone wants a pretty smart investment, it would be worth putting money into building infrastructure. I can't see how anyone could fail to make money, meaning it's another reason to build - and remembering that the cost to build is spread over many years, and an awful lot of that money is paying people (jobs) and businesses, meaning a large chunk comes straight back into the economy through taxes and VAT.