Re: The annoying thing
we'd get the money back many times over in a boost to the economy
No we wouldn't. Whilst Keynesian stimulus has been misapplied to the point that it looks like it doesn't work, the simple and rather unattractive reality is that mixed-to-low tech physical infrastructure projects give the best effect for the economy.
If you pour the money into science and technology, you create the sort of opportunities that the UK has persistently been poor at monetising, you need to focus on top global talent, at the first line you're employing people with higher propensities to save (good in the historic longer term, but bad if you want to stimulate the economy now). HS2 is a misbegotten mess, but it will employ tens of thousands of manual and blue collar workers, as well as engineers and white collar experts. Spending the same money on "pure tech" might get you a few fancy buildings in expensive locations, but otherwise does nothing for the majority of people in the labour market.
The best approach would be more structured support for the tech sector, but not willy-nilly "investment" because that always involves civil servants picking winners and subsequent failure, and then an infrastructure programme in the stuff we actually need and use, so road investment rather than a third rail route between London and the Midlands. It might also make sense for government to start building houses given that the current system is failing to keep up with need. And we could save money by canning vanity Eco projects like Hinkley Point C, and just building a heap of new, low cost CCGT.