There is definitely waste, but just cutting funding isn't going to change that (as we've seen over the last eight years). The critical barrier to this functioning as they claim it should is that the people who decide where the cuts fall are the people who make all the money. Things are never going to become more efficient when the people deciding what needs to go are the people generating all the excess. Trying to get someone with more objectivity to decide is also fraught with problems because that usually entails bringing in one of the big auditing/accountancy/whatever firms and they're horrific for just doing whatever keeps them in a job (a job that is decided by those in charge, and we're back to square one).
In terms of taxation, I'd be happy to increase income tax for higher earners. And I say that as someone who (briefly) did earn quite a bit - when I did some contracting work for Sky, out of a month's gross pay of £9300 I saw £5200 after tax, NI, and student loan repayments. Unfortunately I wasn't earning like that for very long
I also think there needs to be a lot greater resource poured into making sure people do pay what they owe (at the top) because far too many very well paid people are dodging the tax they owe through (often perfectly legal) tax vehicles. Whether it's corporate or personal, HMRC is woefully under-resourced, under-powered, and under-motivated to really make a dent in these entities.