It wasn't just unwillingness, it was the dire economic situation caused by the great depression. It was clear that Germany was re-arming as early as 1935 and while that was a breach of the Treaty of Versailles, it was not considered problematic in itself. A lot of people at the time felt that the treaty was unduly harsh on Germany and the rise of the USSR meant that Germany re-arming was accepted or overlooked on the justification that they needed something in case the USSR did the Commie thing and went for world conquest. More pertinently, the French and UK economies were in shambles and with a very shrunk tax base the first priority was not to throw money on defense expenditure, especially not when your economy was leaking like a sieve and you needed stimulation efforts in other areas.
The other problem was the sheer extent of the German re-arming effort. Tooze in Wages of Destruction estimates that as much as one third of the German GDP in the late-30's went towards military expenditures, this created massive deficits in the German economy that were initially solved by Schacht's financial black magic (MeFo bills being among the more notable ways of keeping the economy floating) and after 1938 by liquidating the gold reserves of Austria and the Czech republic after their annexations. In essence, the German economy was artificially inflated by the massive demand for military equipment but it was never sustainable. The only way for the German economy to remain afloat and not implode under the massive national debt was to go to war in 1940 at the latest. Germany went to war in part to postpone its imminent bankruptcy and had they actually won they would have faced a debt crisis that makes the UK's post war debt situation look like a minor IOU. A side note here is that this is part of the reason why the NSDAP was so eager to promise lands, labor and equipment from defeated foes to their domestic industry, as it was a way to pay off the debt without having any money. The Nazi economy was from the very outset an economy that could only be sustained by plunder in anything but the short term.
Why was this a problem for the UK and France? Because they obviously couldn't match Germany's military expenditure. They couldn't do the Hitler Play and gamble everything on winning a war to seize the national assets of their enemies to pay off debt. They could only shake out re-armament funds from the meager, battered economies they had and that meant that the earliest re-armament efforts, as early as 1935-1936, were pretty sad affairs due to economic reality. Keep in mind that when the war got going and the UK went into war economy, it did not care for minimizing debt accumulation and the end result of that was billions of pound sterling in debt both to domestic industry and to the US for all the Lend-Lease equipment the UK had bought. That debt was the driving force behind the dismantling of the Empire and had it not been for the Marshall Plan the UK would have been fiscally boned for decades afterwards. There was simply no way either France or the UK could have re-armed faster while still retaining their economies. If they had and Hitler had backed down, they would have consigned themselves into yet another disastrous recession before they had recovered from the Great Depression.
It was simply not a realistic possibility to spend more money on the military. The way the UK set up its re-armament, with the Shadow Scheme and similar contingencies for rapidly expanding their armaments industry in case of war, was probably as good as they could get with the economic restraints of the time as it allowed for a small upfront investment but the possibility to go full hog should there be a sudden demand for advanced military equipment.
Sorry for the long post, this is just a topic that fascinates me.