Dissovle the monarchy and have a President
One of the arguments that pro-monarchists have for having a monarchy is that if we dissolved the monachy it would coast more to have a President that would pretty much do the same job. But why would we necesarrily need to have a President when a Prime minster (or just a President that would carry on in the official political capacity of the PM) would suffice on It's own.
The US for example has a President and this was a country which was a colony and a part of the commonwealth. They've managed fine with just a President who basicly represents the country as leader and an ambassador as has the Vice president. And how much more would that cost? Nothing I would think considering we're already paying for the Prime Minister that we have now. At least in the long run. How much it would cost the British taxpayer to dissolve the monarchy is another issue.