BT Vision is a proprietary TV/Phone/Broadband service marketed in the UK: AVS is a North America-centric forum, so few of us here would have any experience with the service or related decoder boxes. I'd never heard of BT Vision until your question appeared today: the closest parallel in USA would be something like AT&T Uverse.
Anyway I took a quick look at the box instruction manual, and under "troubleshooting" it does indeed agree with what jjeff suggested: some (but not all) BT boxes shut down or alter the SCART output when an HDMI cable is connected to the TV. The workaround is to use either the S-Video connector + RCA L/R Audio, or unplug the HDMI when you need to record something via SCART.
Also, you may need to coordinate the output resolution of the BT box to match the device you have connected. If the box is set to "High Definition 720p or 1080i" over HDMI, or "4:3 - Standard Definition," the analog SCART outputs may revert to black border letterbox. Try going into the BT Vision resolution menu,
and change it to "16:9 Widescreen - Standard Definition." This might correct the problem.
Check your DVD recorder setup menu: this also needs to match the box output, or you'll get black borders. Be sure to select "16:9" as the recording default, and choose "16:9 TV" as the display option. Both settings must match.
All of the above applies primarily to TV shows. If you are seeing this problem mostly with movies, another issue comes into play. Many current movies are shot in wider screen formats that 16:9, they can go as wide as 2.35:1. When such films are shown on FreeView broadcast or satellite, they are not always cropped to exactly fill a 16:9 television. Instead, they will fill the screen from side to side but you will see black borders along the top and bottom. This is normal and required to show 100% of the wider image: studio DVD and BluRay releases are formatted the same way.
When "letterboxing" is the problem, it usually manifests as black borders on the top and bottom plus thicker darker black borders on the sides of a 16:9 TV screen, so that you see a shrunken 16:9 image surrounded on all sides by black (the zoom control on your TV will fix this by enlarging the smaller image, but PQ gets degraded). In USA/Canada, more and more cableTV and satellite services are forcing letterbox framing over analog outputs, which perversely shrinks even standard old 4:3 programmes to a postage stamp in a sea of black borders.
You might get additional, BT-specific help by posting directly to the BT Vision user forum, which you can find at this link