I always buy/bring paper maps. You can't get a good oversight on an average laptop screen, let alone on a phone. I like to *understand* the geography, not just follow directions.
btw, for anyone coming to or cycling in London, I've just discovered that Transport for London (tfl.gov.uk) issues a series of free cycling maps you can order by mail. They're really good - each one covers a substantial-sized section of the area (extending quite far into the suburbs) and indicates all the bike paths, both on and off-road. They're printed on quite substantial paper, too, and don't have the A-Z problem of always cutting off the page right where you are (I don't know how to A-Z does it; it's quite remarkable!).
wg