What's the earliest Broad Bean?

I'm looking to get an early crop of broad beans in my polytunnel.
I want to take them to maturity to harvest dry, but still leave enough time to get other crops in the space mid/late spring (probably tomatoes at the end of May).
The PT is run along 'no dig' lines, meaning that the growing medium is mainly well drained, but water-retentive compost, and certainly not the cold/wet clay beds that I have on the rest of the plot.

My intuition says to start them in pots at the very beginning of October then plant them out.
Wind isn't a problem so tall varieties can be staked.

Any advice on planting and varieties? Looking for maximum yields from an overwintered crop. PT is high enough to support a tall variety.

Thanks

Philip