Hello,
I am looking to book a flight from London to Austria that goes through Hamburg, Germany. Is a 35 minute layover enough time to transfer planes at this airport?
Thank you!

Hello,
I am looking to book a flight from London to Austria that goes through Hamburg, Germany. Is a 35 minute layover enough time to transfer planes at this airport?
Thank you!

Where are you flying from and to? If you are buying with the same airline on the same ticket then even if you miss the connection they are required to get you to your destination and if hey are selling this ticket then they think you will make the transfer.
To short for me to be honest and even if you make it I suspect if you have a bag in the hold i doubt that will.

Not only what #1 wrote but also think about if your first plane come some minutes delated - if it's not the same ticket you will have a problem.

You are just within the Minimum Connecting Time of 35min (http://www.haminfo-terminal.com/technical_information.php), therefore, if you are on one ticket, no needs to worry (in case of delay, the airline will take care).
You baggage of course needs to be check through.

35 minutes is exactly the minimum connection time Hamburg Airport gives - so its technically possible. Just keep in mind that you have to go through immigration at Hamburg, since London is outside the Schengen area.
If it is on one ticket, you should be fine, as it is the airline' s responsibility to arrange alternatives. Still it is your task to proceed as quickly as possible straight to the gate.