I don't know about price, but Scorpion was a destroyer, not a battleship.
I suspect that it's almost an irrelevant question, though. The Royal Navy was not subject to the sorts of massive ammunition spending that the Army was; shell shortage was a land-war problem in the Great War. I vaguely remember reading - sorry for no source - that it took an incredibly long time for the Royal Navy to run through its prewar munitions stockpiles, even for the destroyers, the workhorses of the fleet. Ammunition, for the destroyers of 1915, was virtually a sunk cost. Maintenance was not, but I suspect weapon maintenance wasn't so significant a problem that the Admiralty would've raised an eye over a bit of camel target practice. It's not like the Admiralty was short of funds.
Which leads us to the real point: there wasn't really a budget. Britain, and the other major belligerents, voluntarily gave up control of military expenditures at the outbreak of war, essentially giving procurement carte blanche to purchase whatever it felt necessary to win (and, eventually, "whatever it felt necessary to reduce our casualties"). Virtually any expenditure, regardless of waste, was justified. High casualties came in for massive opprobrium in Parliament and the press, even in actions that were theoretically 'victories' (to say nothing of the defeats). High expenditures for no purpose were virtually ignored in the war; few people criticized the massive Somme artillery preparation on the grounds of financial waste but rather that it had been insufficient to prevent massive casualties on the first day of fighting. Other outrageous expenses, like the hundreds of millions of pounds pumped into the Arab Revolt in bribes for the production of virtually no military value, were similarly justified on tenuous grounds.
When the Americans attempted to force the British government to control its massive spending in late 1916, the Ministry of Munition was confronted by a run on the pound, a massive fall on the City exchanges, and the Damocles' sword of an end to Britain's ability to purchase American goods. Even this apocalypse did not slow spending one iota. Instead, Britain was saved from having to confront the problem by Germany's resumption of unrestricted submarine warfare, which brought America into the war and removed the possibility of a financial disaster before the armistice.