Connection at Dusseldorf
 

I am looking to book an inter Europe flight withe Lufthansa from the UK, which will give me a connection time if 50mins at Dusseldorf, is this enough time.

It may do depending on if it is the same airline throughout. I flew Air Berlin a few years ago to Munich & at Dusseldorf they just transferred us through the transfer gate & it took around 10-15 minutes, we didn't have to pick up baggage or any thing.

DLH flights at DUS all operate from the same pier and it's not too long, so you should be ok with 50 mins IF your flight departs the UK on time. If there is a delay I'm sure DLH will take care of the problem.

Is there a passport check in DUS? Things might get a bit stressed when you have to be pushed through immigration and security checks to make your plane in 50 minutes.
But if you book it as one trip, it's the airline's problem to get you on another flight if you miss the one you planned.

I just connected both ways on a ZRH-DUS-ORD round trip ticket and the connection was painless in both directions. It's a nice little airport and if you stick with LH on both legs the transfer is a doddle.