HDMI is a purely digial interface standard designed for HDTV. It not only carries the digital picture and surround-sound signals but also the copyright protection information and device control signals for suitably matched 'boxes'.
The SCART system was developed about 20 years ago as a means of carrying purely analogue signals consisting of Stereo sound and pictures in one of three different video formats: S-Video, Red/Green/Blue and Composite. It also carries a basic form of device control signal. It cannot carry HDTV or "Component Video" signals.
SCART cannot carry HDTV signals. However, the BT Vision box is not an HDTV source because the material is derived from Freeview (which is still not HD) and they don't transmit their pay-per-view stuff in HD. (see link below).
You cannot create HD detail where none exists, so in practice, you will not get any improvement in picture from using HDMI cables out of a BT box. The pictures that you will get will still be very good.
Spend your money on a good SCART cable for your Bt Vision box and leave the HDMI socket on your telly free for a genuine DH source such as a Blu-ray player or Sky HD box.
Note that it is not possible to have a cable with an HDMI connector at one end and a SCART or phono connector at the other. The electrical signals are not compatible or interchangable.