With regards to train travel - Virgin West Coast and Midland Mainline are both signal black holes (mainly down to the trains), while Central City Link (Nottingham to Manchester) goes through a number areas that have no DAB signal (or FM for that matter). No idea what the signal is like in the south (generally the older the train the better the reception)
DAB does have the equivalent of RDS....
Firstly :-
The national stations (all BBC except local and nations, Capital Life, Core, Classic FM, Life, Planet Rock, Virgin Radio, talkSPORT) use the same frequency nationwide (the commercials are on a different frequency in Scotland) so don't require retuning (when you are in overlap areas the radio uses the signal from both (or more) transmitters to it's advantage). Within a local or regional multiplexes coverage are you won't need to retune either.
If you are travelling between local multiplex areas...
1. You will need a radio that auto retunes (my JVC car unit does, my Pure handheld doesn't).
2. Common PIDs (NOW Digital do this on all the ex-GWR multiplexes in central and southern England) - this allows you to stay listening to XFM Midlands, Chill, Traffic Radio, Smooth Radio 106.6, Heart 106.
The muppets running the northern Emap multiplexes havn't bothered with this (which means that as you pass Bolton services on the M61 you'll need to retune your radio to continue listening to XFM Manchester)
3. In liue of Common PIDs you'll need a radio that supports LSN, and multiplexes that does as well - As far as I can tell this hasn't been implemented as yet
On my in car radio I don't lose the signal of TWG-EMAP Stoke though the tunnels in Stoke-on-Trent, but I do lose the national multiplexes - tunnel reception is down to transmitter location, tunnel construction and receiver sensitivity.
IIRC only 40% of the UK population has national DAB hand held coverage (compared with 85% having portable outdoor reception (i.e. in car)
Saying all of that, it looks like you will be staying within the coverage area of the NOW Sussex Coast multiplex
http://www.now-digital.co.uk/SussexTX.jpg so none of that actually matters, although there is a signal blackspot near Berwick on the A27 where you may lose the signal.