A BBC Radio 4 consumer programme compared the battery drain in DAB sets with that in non-DAB ones and found that it was typically 14 times higher. So, if you're buying a mains-battery set and (while away from a mains power source) wanting to listen to a station that's available both on FM and DAB, it's definitely best to go for the FM option.
This link seems to include all of my favoured brands:
https://bestradios.co.uk/best-battery-powered-radios/
My mains-only internet radio (with DAB 7 FM) is from Majority and I'm really impressed with the quality, so that's definitely a make to consider.
I also own a Goodman's Canvas radio, which is among those listed there and has remarkably good sound quality for such a small radio. (Note that the info on the link states that the batteries only last for about 10 hours but that's on DAB. If you follow my advice to switch it to FM, they last much longer).
Roberts radios are also included in that list. They've long been recognised as a premium brand, with excellent sound quality, although at a price.
My own recommendation would be to go for any of the DAB radios shown on the Majority site:
https://bestradios.co.uk/best-battery-powered-radios/
(They all offer FM as well, so that you can avoid excessive battery drain). In particular, you should note that the Girton model uses 'C' batteries, rather than 'AA' ones, providing longer life, and that the Eddington is rechargeable from a USB port, dispensing with the need to buy batteries altogether.
So my absolute TOP recommendation has to be the Majority Eddington:
https://www.majority.co.uk/radios/eddington/