Well the thing is it all depends on how you think about empire. Empires lose and gain territory all the time. It's one thing to be substantial, but ultimately what we mean by empire is strength and breadth of influence, within which there is the crucial factor of cohesiveness. The OED defines this kind of imperialism as "A policy of extending a country’s power and influence through colonization, use of military force, or other means". So when you look at whether the British (or any) Empire was in decline, you need to look less for the losses and gains of territory and more at how it was holding together as a whole. When big empires collapse, it tends to be because of a mostly gradual decline in the ability to maintain cohesiveness and strength of influence across the entire empire, which ends in a sudden final disintegration, and the British Empire was the biggest. So I'd argue that you need to look at the colonies' attitudes towards Britain, the ability of the British to deal with it effectively and to some extent the perception of Britain by Britons themselves.
There are arguments which say that Britain declined over the entirety of the 20th century and beyond - the 1997 Hong Kong 'Handover' was a seminal moment, although Britain still holds groups of islands today; the Commonwealth hasn't really been just another name for empire since the 1930s. I think it was 1931 when the British Commonwealth became just the Commonwealth. Even before 1900, the Dominions (e.g. Canada, Australia) were starting to pull away and feel distinct from Britain. It's possible to argue that the British Empire was in wider decline over various periods of time. For instance, Britain would have had a much harder time with both World Wars if the Dominions hadn't agreed to help. In other words, Britain's influence, along with other imperial powers, was certainly at least on its way to becoming a sham early in the 20th century; even if Britain and the other powers weren't yet fully aware of it. The British Empire was at its biggest extent following the mandates it gained after 1919. Yet I think even that term - mandates - indicates how times were changing. These were not official acquired territories. They were areas which Britain had, ostensibly, agreed to manage for a period of time following the fall of the German empire.
In terms of colonial revolts, before 1914 there were tensions building in, to my knowledge, Kenya, India and Zululand in South Africa. The Kenyan Mau Mau revolt grew in earnest following the war, but things were building. There was an Indian revolt before the one in the 1940s, in 1857, which failed. Then there's the famous defeat of British colonial soldiers at Isandlwana in 1879, followed on the same day by a victory against all odds by the British at Rorke's Drift. Britain's modus operandi was increasingly, well before 1914, to use primarily a territory's own citizens for its government and military presence in the area, with British officers and officials in charge. Britain was too small a country to be able to exert a purely British authority over 1/4 of the world, and because unrest was growing across the empire from the mid-1800s Britain was thus beginning to struggle with its empire, even if it didn't realise where it was all going yet.
The British didn't really see themselves as not imperial even after 1960; not in popular culture. Mary Poppins, made in 1964 in America, talked about how everyday Britons could be part of 'railways through Africa' and 'dams across the Nile', and how children needed to be raised to aid the empire. It was set in the early 1900s, but films always tell you much more about who made them than what they're commenting on. I.e. that Britain still had an imperial image. The James Bond franchise, begun in the 1950s, arguably portrayed Bond as the defender of a 'still-active' empire, as Black put it. He notices that Bond stories were never set in recently-independent areas of the empire, or in the Dominions, and featured Bond defending British interests overseas. That franchise continues, updated, today, and we still don't question that Britain should be interfering overseas or that its interests clearly lie there. If Britain wasn't part of the nations 'peacekeeping' around the world, we would find it very odd. Deighton talks about the main legacy of the British Empire being a leadership role in foreign policy. It's one reason there's this big debate about the EU in Britain - to a lot of people it feels like giving away the autonomy which Britain should without question clearly have.
However, there are also arguments which say that the British Empire ended rather abruptly and cleanly over a few decades from the 40s to 1960 or so. On culture, British historical education started with Caesar and Rome until at least the 1950s and today doesn't even mention empire. I'm not sure at which exact point it changed, but it links in with the continuation of imperial identity until the 1960s. Looking at political cartoons, newspaper articles, Conservative electoral manifestos and the evolution of the Foreign and Commonwealth Office, it seems to me that empire stops being overtly discussed at a pretty clear point in 1960-1962. Things just came to a dead stop. In 1962 a plan was proposed to begin consolidating the various international relations into something similar to the current Foreign and Commonwealth Office, the first stage of which was completed in 1964. People stop using the term 'empire' at official and media levels after 1960. I think the last manifestos to include the term 'empire' were in the 1950s. The.... 1959 one probably didn't and the 1964 one certainly didn't. People still talk about the Commonwealth, but 'empire' wasn't in much use. Moreover, Britain gave independence to India, its crown jewel, in 1947. Whilst it still had African and Asian territories, that was the big one. Many other major instances of independence happened around this time, and then more happened into the 80s and 90s.
So... it depends on your focus. If you're looking for the very beginnings of decline... well I'm sure someone could make an argument that the beginning of empire was the beginning of its eventual decline. I'd argue that short-term decline is to be found in the 40s and 50s, and that mid-term decline goes back into the late 1800s and long-term decline over the 19th century generally. This is mostly specific to Britain, but the wider trajectory of European colonial empires goes roughly along that track. Ultimately, I think that the international relations leading up to the first world war, and then the mandates following the war itself, probably sent the empire into terminal decline. Britain made a huge amount from its shipbuilding industry, but because the Kaiser wanted a navy (which he didn't seem to realise would challenge Britain's three-power standard for naval dominance, which was the fundamental cornerstone of British imperial influence) Britain then ended up spending inordinate amounts on ships to keep up the numbers. Eventually they build the Dreadnought, which made all other ships obsolete and unintentionally gave the Germans much more of a chance of challenging Britain's naval dominance. This, with the war on top of it, went a long way towards running down Britain's finances. Just when it was trying to get back on its feet, you then get Britain taking on even more responsibilities. I don't think that Britain could really afford to do that. The problem is that empire was still the ideal at that point, and at 33,700,000 km² compared to France's 12,347,000 km² Britain's empire was almost three times the size of France's one - the next biggest. Britain had an image to maintain - that influence again - and so ironically I think Britain ended up costing itself influence by trying to maintain its international image. So there is clearly decline before the first world war. It's just that if you're looking for the moment of collapse, you need to look at the 1940s and 50s.
I can't really give any evidence for a pre First World One decline as it isn't something I have ever encountered but here are my thoughts.
Perhaps what you have heard about a decline in British power before the Great War is based more on an increase in the power of other Empires and Nations ie the rise of the USA, Japan, Germany. Relatively speaking Britain isn't in decline but its power is still diminished due to the increased power of others. As I said I have not heard any arguments for this before so that is a stab in the dark.
As for counter arguments, the British Empire reaches its largest extent in the years after the end of the First World War after it gains mandate territories in the Middle East and Africa this would counter a point about a prewar decline. During the war Britain mobilised the resources of its Empire in order to fight the war, an Empire in decline would not have been able to achieve this.
Well, there is some rather concrete evidence that the empire had begun to lose territory, in substantial amounts, by 1783.