Were there attempts to form a Popular Front, à la those in Spain and France, in Great Britain in the 1930s? Why did these attempts fail? Did the Labour Party push for or resist attempts to form a left-wing coalition?

The Popular Front idea did get some traction in Britain, but the configurations of British politics of the time didn't exactly lend themselves to it coming to fruition either conceptually or practically.

As with many other places throughout Europe, it was the Communist Party (of Great Britain, or CPGB) that were the most consistent advocates for the Popular Front idea. The CPGB's policy and approaches reflected the wider strategy of the Communist International (Comintern), the Soviet-based agency that coordinated global efforts to bring about world revolution. CPGB tactics were, if not quite dictated from Moscow, heavily influenced by the Comintern 'line', which after c.1934 emphasised the formation of alliances with other progressive elements in order to resist fascism domestically and internationally. This was the basic idea of the Popular Front - by cooperating rather than competing with other leftist organisations, they would maximise the left's electoral success overall. It was hoped that a series of Popular Front governments across Europe would then commit to a credible collective defence against fascist aggression, in cooperation with the USSR, thereby containing fascism.

This idea, as you note, saw some success in Spain and then France in 1936, which added to the momentum behind the idea in Britain. The catch, of course, was that British politics were rather unlike both France and Spain. For one, while British conservatives were hardly steadfast opponents of fascism internationally, there were few immediate prospects of fascist electoral success within Britain by this point, with 1934 marking the limited peak of fascism's fortunes in Britain, which in any case was relatively poor soil for such a movement. For another, while Spain's electoral system in particular encouraged joint platforms and electoral pacts, Britain's (mostly) first-past-the-post, constituency-based system tended to reward smaller numbers of stronger parties. Most seats were already straightforward competitions between two parties - electoral pacts, with a few exceptions, simply wouldn't change the dynamic that much.

So, while the CPGB continued to push for a British Popular Front in 1936, it was not met with resounding enthusiasm from most quarters. Cooperation between the tiny Communist Party and the very large Labour Party offered little for the latter, who were in any case highly distrustful of the CPGB (not least because the CPGB had spent most of the last five years decrying Labour as 'social fascists' propping up a broken capitalist system and getting in the way of revolution). Labour's rejoinder to communist entreaties to form a progressive alliance was to point out that Labour already was a Popular Front - constitutionally, Labour was born as a federation of affiliated organisations and parties rather than a monolithic entity, and by the 1930s still represented a meaningfully diverse set of institutions and interests, albeit in an increasingly centralised way.

This gave the CPGB an opening - they would apply for affiliation to the Labour Party directly. The union and party officials running Labour were generally staunchly anti-communist and not at all interested in negotiating such an affiliation, so the CPGB set about convincing the Labour rank-and-file, hoping to win over enough delegates to force through a motion at the Labour Party annual conference allowing the CPGB to affiliate to the Labour Party. This motion was eventually tabled at the 1936 Labour Party conference (held in Edinburgh in October). This moment represented the best chance the CPGB had of achieving its immediate aims - passions were running high following the outbreak of the Spanish Civil War in July, which had resulted in an outpouring of solidarity from British labour movement for the Spanish Popular Front government, and discontent at the sometimes tepid response of the Labour Party. Nonetheless, the motion was still defeated by a large margin - 592,000 for, 1,700,000 against.

In the aftermath, the CPGB set its sights a bit lower. In January 1937, they declared an alliance with two other left-wing groups, the Independent Labour Party (a former Labour affiliate which still retained a handful of seats at Westminster) and the Socialist League (a soon-to-be-expelled-for-cooperating-with-communists Labour affiliate). The ensuing Unity campaign was short-lived - the Socialist League collapsed soon after in the face of Labour's punitive measures, while events in Spain from May 1937 drove a wedge between the CPGB and ILP. While it remained CPGB policy to unite the British left until 1939, this was the high water mark of formal political cooperation across parties.

As a postscript, there's a school of thought that the grassroots energy supporting unity was channelled by the CPGB into the growing 'Aid Spain' movement instead, with 'embryonic' local Popular Fronts achieving local cross-party cooperation in support of an anti-fascist cause. While cross-party support for this cause was certainly achieved, and the CPGB certainly liked to think it was all part of their cunning plan to win over Labour's grassroots, most scholarship in the past 20 years or so has cast doubt on the extent that these local coalitions were anything near as robust or even politicised enough to be meaningfully considered even nascent 'Popular Front' organisations. While my own view is that there were some local conditions where this wasn't necessarily the case, the structural constraints on the CPGB were such that it was an inherently self-defeating strategy - meaningful cooperation was only ever be achieved in political spaces where the CPGB was weak enough to present no electoral threat whatsoever.