There were questions asked, in a literal sense: most returning volunteers were interviewed twice by gvernment officials. The first instance was in Spain, before they left - virtually none of them had valid travel documents, so needed to be issued with emergency passports in order to travel home via France. The second was after crossing the border, where they were usually interviewed by Special Branch types about what they'd been up to in Spain, were the communists and so on. Individuals answered these questions both honestly and dishonestly, but were not arrested. Being a communist wasn't actully a crime, while the relevant legislation - the Foreign Enlistment Act (1870) - was of dubious applicability in the circumstances, as Britain had not recognised either side of the civil war as a belligerent. This has been realised in early 1937, as volunteering reached its peak and various criminal investigations were opened in to potential breaches of the Act. Rather than risk an embarassing defeat in the courts, the government opted to sternly caution British citizens against joining in the war, but took few practical steps to actually prevent them doing so.

I've written on here before about how the returned volunteers were treated by the state during the Second World War, which is a subject of longstanding controversy given that most of the returned volunteers had been motivated by anti-fascist beliefs, which was now the official wartime position as well. I've also actually published my own research on the question, which is linked in that post. While there was some, highly variable prejudice or restrictions (such as potentially being blacklisted for employment in sensitive industries), this was generally due to their pre-existing political beliefs (ie communism) rather than their activities in Spain. Few were arrested, and generally not for their political activities. One returned volunteer, David Springhall, was arrested, charged and imprisoned for spying for the USSR in 1943 - he had been caught receiving secret documents from a RAF employee. Springhall was, by all accounts, guilty as hell, and was actually expelled by the Communist Party of Great Britain after the incident - I think British communists genuinely had no idea he was mixed up in espionage. This was rare though - most members of the Communist Party stuck to legal forms of activism, and as we now know, the most successful communist spies of the era were those whose affiliation remained entirely unknown.