It depends what you want from a holiday really? I have been to Jutland many times on camping holidays with my wife and kids, and although i wasn't to keen at the start, i have begun to understand what makes the place so special - and that is not the warm weather and cheap ale! I have also been to the Central Island of Funen and spent time in and around Sønderborg and have enjoyed them all. However, if you want access to the internet 24/7 and entertainment in the evenings i would look elsewhere.
Most Brits tend to like the sun, cheap booze and access to Premiership football whilst relaxing by the pool, so if this is your ideal type of holiday, i would avoid the Denmark. The beer is expensive in the pubs, the climate is similar to the UK and it costs a lot more to eat out than it would in most other places in Europe. However, on the other hand, the quality of living is high and the facilities in most places are exceptional. Because it is not a cheap place to "get on the piss in the sun" it does not attract people who want instant entertainment and a cheap place to stay. Food in the supermarkets is about 10-15% more expensive than what it would cost in the UK but wine and spirits are about the same price. For some reason beer tends to be more expensive and the quality isn't great (Tuborg and Carlsberg). Its perfect for nature lovers and the place is very safe and child friendly. However, it can be perceived as boring by most people because its a family orientated place and there is not much going on after about 2000hrs in most places around Jutland (family time).
The campsite we usually go to is Hvidberg Strand on the West Coast of Jutland, just outside a the small town of Blavand. It is not cheap but it does deliver and it is situated right next to the beach. You won't find many Brits over there though.
If you want any more info just send me a pm.