How about I answer this one?
Me not being British at all, a proud Irishman, socialist and democrat fyi. As an aside, Ireland is probably the best comparison of what a republican Britain would look like. Ireland's political system is almost a direct clone of the British system c1920 - with the monarch replaced with an elected President and the House of Lords replaced by a Senate.
First of all, the monarchy is cheap. Really cheap. The royal household costs the taxpayer ~£30m a year. It's a pittance per person (In the region of 70p). This money is more than clawed back in various tourist and merchandise related taxes and jobs gained. Cost is not an argument against the monarchy, more an argument in favour.
Second, the monarch is a unifying figurehead. It is an apolitical symbol of Britain's proud past and traditions. The pomp and circumstance surrounding the monarchy is as positive a display of nationalism possible. People from across the political divide can be proud of their monarchy. Elections can be divisive and bitter and about personalities. And that's even when you have serious policy issues to debate. Now imagine the election was for a position that had no policy powers (The Irish President for example). What is there to discuss besides personalities? Our Presidential Elections have a habit of being very bitter affairs (the previous one ending in the most bitter fashion with a live-on-TV decimation of the front-runner by Sinn Fein calling into the debate's producers and supplying incriminating information without any evidence).
One only has to look at Britain in the 30s and 40s to see a nation that rejected fascism, had political unity and a monarchy that held public resolve together even as the bombs fell and defeat seemed imminent.
Philosophically I disagree with monarchy in the hereditary sense, it is elitist and anathema to a equal, democratic state. But speaking pragmatically, the monarchy's benefits to Britain far outweigh its negatives.