People don't tend to invest so much in stocks, instead settling for other instruments, like ISAs that already handle the tax end of things (https://en.wikipedia.org/wiki/Individual_Savings_Account). ISAs are an attempt by the UK government to encourage saving / investment by providing tax incentives to do so. Again, tax considerations done upfront vs after-the-fact.
If you do invest in stocks, you're liable for capital gains tax, just like in the US, but whether you need to file or not is dependent on how much you actually made. If you make too much, you'll have to file taxes yourself, but it's relatively straightforward.
The point is not that the system is perfect, but that it handles the case for probably >90% of the population, without stress or complications for them.
There is no personal benefit.
For cash gifts the charity can claim back 25p in the £ on your gift. For property, land and shares you deduct it against your tax payments at the end of the tax year and claim for a refund.