Well I'm a happy bunny; got home from work today and followed your advice purecain. I can't find an XFX .bin file with the bios for an HD 4870 1GB, so I looked on the VGA bios database, and downloaded the sapphire version for the card (chose this cos it looked more recent than some of the others). Copied this onto my bootable USB, booted from that into DOS, used atiflash to flash the sapphire bios onto my card . . . at this point I had to use the -f flag to force it which made me a bit nervous. Rebooted the machine and to my relief and happiness it's working perfectly. Wonderfully, the original problem I had which started all of this off - namely the flickering on the desktop - appears to be fixed too. I'm very happy.
Thanks so much purecain, w1zzard and everyone else on this thread for your help, please know there are lurkers out there who really appreciate it
To anyone else who has reflashed a bios and still not getting any joy, it's probably worth trying a couple of different ones before you give up.