First question to the OP: what type of aerial and aerial amp do you have? If it is like my Bailey it will be a Status 570 aerial and a VP3 aerial amp. If so then you are well over half way there. Earlier Status aerials would only cover 88-108MHz for FM radio, and 470-860MHz* for TV, but not the 170-240MHz for DAB in what is known as Band 3. (*Due to the sell-off of bands 4 and 5 for 5G and 4G mobile phone use respectively the upper limit of the aerial reception range will be 706MHz or 790MHz depending on the age of the aerial.)
Per the radio, you may have difficulty finding a car radio (usually with CD player) as many car manufacturers have moved over to the so-called 'Infotainment' units that are basically a computer that is part of the vehicle management system with an embedded FM/DAB radio. Halfords sell a Sony MEX-N7300DB which seems to have everything - DAB/FM/MW/LW, Bluetooth, USB, CD, even voice control but you will need to do a bit extra to fit it.
For a start It needs two aerial feeds, one for LW/MW/FM and a separate one for DAB. The easiest solution if you want to hear everything is to fit a Vision Plus LW/MW/FM telescopic aerial. VP no longer list them on their web site but you will find many dealer shops still have them in stock. If you go down that route then all you need for DAB is a feed from the aerial amp. However remember that many AM systems are dying out - the most important being (R4) LW on 198KHz from Droitwich which formally closes at the end of June this year after over 90 years service so AM may be worth giving a miss.
If all you want/need is FM and DAB, then the Status 570/VP3 or VP5 will suffice, but here you will need a splitter. VP do a suitable device with the correct connectors - all you will need is a length of cable to get from the aerial amp to near the radio with F-type plugs on both ends which you can make up yourself - parts from Toolstation or Screwfix..
Just beware of one thing. TV in the UK is both horizontally and vertically polarised on a per-site basis, so your receiving TV/radio aerial has to match same. ALL DAB transmissions are vertical and are not necessarily transmitted from the same site as TV. If your TV signal is vertical then DAB will work (usually) quite well as the DAB part of the aerial works as omni-directional in those circumstances, but if the TV signal you are using is horizontal you may find DAB difficult to use (the 'bubbling mud syndrome') if the signal is poor.
Finally, I have just seen that some Swift and Lunar caravans are only fitted with a TV feed - the aerial and associated amp do not pass FM or DAB signals. If that is the kit your van has then you may find it will be an expensive job as you will need to change the aerial and amp as well! In such case a portable FM/DAB radio may be a significantly cheaper option, or as another contributor suggested, use your mobile phone as a feed (by cable or Bluetooth) to a wi-fi/Bluetooth speaker. From comments on here the Bose Soundlink 2 is very good albeit expensive. A make I find to be acceptable are those made by Anker, but note that if you want proper stereo you may need two units in some cases!
Good luck.