[4candles]

Assuming you have good FM reception, then record the FM broadcast - it will be infinitely better than your DAB radio, which only uses 128kbps for Radio 2 (and most other music stations). The best digital version of Radio 2 will be the 192kbps satellite stream (or the 192kbps "Freeview" stream), but even those are probably not as good as a decent FM recording.

However, the BBC use NICAM digital links to feed their network of FM transmitters (NICAM is 14-bit, 32KHz PCM audio, transmitted using a lossy compression scheme reducing the 14-bits per sample down to 10 bits per sample - a system that's also used for transmitting digital sound with analogue TV in most of Europe). So an FM signal is far from lossless, even before it leaves the transmitter.