Many are still in favour of having a Royal Family, and although the point regarding them bringing in money through tourism is probably overstated and exaggerated, it is still a valid point that they do help to increase tourism, you will see for yourself that if you visit tourist shops in London most shops will have a large section full of Royal Family mugs, t-shirts, fridge magnets etc.
Our Royal Family is respected worldwide, the Queen was one of the most highly respected head of states worldwide.
One option would be to phase out the majority of titles and payouts until we have a small royal family with a modest estate. Tax them so that gradually over a period of many years the vast wealth is in the hands of the state, not the family.