Bad news, I think.
The vast majority of BBC programmes are NOT put out on video/DVD because of rights issues. i.e. the contracts with the actors and the production company only give the BBC the right to broadcast the programme, not to issue it on video. To re-negotiate the rights would probably take months of detailed talks with various bodies so, unless a video release was included when the original contracts were signed, you won't normally be able to get hold of a programme.
If this programme was made available on video, I would expect to find it at www.bbcshop.com. It's not there, so either it was never issued or it's been discontinued. Unfortunately, since there doesn't seem to be any reference to it on any of the usual video review sites so I doubt that it was ever issued. (I suspect that the economics of putting 10 x 55 minute episodes onto VHS, back in 1984, meant that it couldn't be offered for sale at a realistic price).
Sorry to be so negative. I'd love to be proved wrong!
Chris