TOPIC:

Was any record kept by the British authorities of their names? So far I've only come across one named in the British papers, a Scotsman named Miller, captured in early 1899. And "we have got 20 men here as Boer prisoners who belong to Crewe, and two belong to Stoke" after the Modder River battle. Several other examples too, but no more names.

This is a very good question, and I puzzled over this... to me, there are potentially 2 categories of 'Briton' who fought for the Boers.
(a) Many Boers spoke English, and some spoke it as a first language. Many Boers were of British descent, and often bore a British surname. Many British had resided in the ZAR and OVS Republics and had become citizens. } All of this group were Boers by nationality, though the British newspapers may well have been indignant.
(b) Some British men, mainly Irish, were not citizens of the ZAR or OVS, but volunteered to fight on the Boer side because of their ideological views. I don't know enough about the Irish Brigade (Blake, McBride etc) to know how they were treated if captured, and I would be fascinated to know what penalty they faced.
Citizens of the Cape or Natal faced execution if they took up arms against the Crown, though fortunately many were pardoned at the end of the war.
I hope this helps get the ball rolling!
Rob

There were also some Britons who were forced to join the Boer forces; it's possible that some took steps to make sure they were captured by the British, if they got the opportunity.

....A young Kent man, who is now serving with the Boers, and who for obvious reasons does not wish his name to be published, has written to his father, who resides near Maidstone, and in the course of his letter he says:— "You will all call me a rebel, but when I was called up by the Orange Free State we were told that we should be asked to defend the country and not invade Cape Colony. I thought it better to agree to these terms, or else my farm and everything else would have been confiscated. But I shall never forgive myself, nor would you if you had seen the poor British mowed down at Magersfontein. But not a man did I fire at. That I made up my mind not to do. You should see our entrenchments, for we burrow under the ground and never get hit. Millions of pounds must have been shot away by the English gunners, and you, father, will have to pay for all the waste. It made me laugh to see the firing hour after hour and not one of our men hit. The English all start their engagement like that. They fire two days, and as they always follow the same childish plan we know they will not attack until after a day or two's bombardment. Then we come out of our burrows and simply shoot them down like deer. But I haven't stained myself with English blood, and don't mean to."
Congleton Chronicle, Saturday 24th March 1900