How do I train for climbing in a relatively flat area?
Can you measure your cadence? (The answer to this is that you can, even if you have to resort to counting strokes and looking at your watch. But a computer will make it easier.)

On the flat, try riding in a high gear and at a high cadence, as much as you are able.

This should translate to lower gear / high cadence when climbing (which is what you want).

A word of warning though, riding in too high a gear can cause knee pain, which isn't good. So you're basically looking for a threshold - the highest gear you can manage, while maintaining a decent cadence (say, 70 to start with, but ideally higher) and without it being painful. 

Something you won't be able to reproduce is the heat - climbs can get very hot as there often isn't much airflow. But as you say you're riding in Yorkshire that shouldn't be a problem ;-)