I'm mostly basing this on reading I've picked up over the years so can't remember all my sources. There were a number of British folks (and loads of other nationalities obviously) who fought for Franco. The book 'Franco's International Brigades' by Christopher Othen is good in covering this. Peter Kemp was an Anglican/Protestant but an ardent conservative and monarchist. He first joined the Carlist Militia the 'Requettes' and later was part of the unified army under Franco. He rose to I believe the highest rank an Englishmen ever did. There was also a Welshman who's name has escaped me. The Catholic community (and Catholic Newspapers) in Britain were in support of Franco after hearing of the atrocities committed by the left wing mobs. Hilaire Belloc, the famous Catholic writer, was in support of Franco and so was J.R.R. Tolkien, however they both began to feel strong reservations after news of atrocities committed by Franco's side came out and were rather dismayed at the whole violent situation.

There was also a South African poet named Roy Campbell who was in Toledo when the Republicans came in and began massacring all his friends who were Carmelite Monks. He was highly depressed and frustrated at how the media was in complete support for the Republican side back in Britain. The papers generally came down heavily against the Catholic position.

Returning to Kemp, he is an interesting figure because Anglicans were generally not on the side of Franco. I remember reading a conversation between George Orwell and an Anglican priest friend of his who asked Orwell about his experiences after returning; he said something like 'I heard the Republicans are burning all the churches' and Orwell replied 'just the Catholic ones' to which the priest was then no longer bothered.

It's also worth mentioning that Oswald Mosley said that 'Spain is not worth one drop of British blood'. The Fascists in Britain did not see the Civil War as one between democracy and Fascism as is often portrayed. In reality Franco was not a Fascist. He was not revolutionary but rather a strict nationalist and conservative who believed he could restore order to a country that was severely divided. He did have a Fascist party and organisation under his command though, the Falange, but he managed to liquidate their leadership and put an idiot in power so he could more readily control them under a unified central command.

It is worth mentioning that I am Catholic and you may of course see I have some biases so take from my post what you will. Read around the subject and don't take one person's answer, including mine, without studying different books and sources. It is still heavily debated in historiography today.

Edit: The stuff about Roy Campbell comes from a book called 'Unafraid of Virginia Woolf: The friends and enemies of Roy Campbell' a biography by Joseph Pearce and it covers the Spanish part in detail. Also 'Remembering Roy Campbell: the memoirs of his daughters Anna and Tess' covers this period.