GBP is as easy to change as USD in Uganda. You can’t spend either USD or GBP in shops, but touristy things (eg hotels, national parks, rafting) will want payment in USD (and they’ll want a lot of it).
Cash machines work well and are all over the place. Visa cards work in all machines. Mastercard you can only use in Stanbic – but there are loads of Stanbics around too, although maybe check if you’re not in a major town. You’ll almost certainly need to phone your bank from Uganda after the first blocked withdrawal (which will possibly be the first one you try), and periodically thereafter, but it’s quick and easy to buy a pay-as-you-go SIM and credit to do this.
You need to hand over a fair wadge of cash (GBP 40?) when you arrive for your tourist visa.
The current political situation isn’t ideal so maybe keep USD 500 safely somewhere as an emergemcy exit fund.
It’s a really safe country (in the safe bits) so don’t worry too much about wandering around (within reason) with cash on you.