Brake Pedal unyielding after overnight stop inhibits starting

Can anyone shed any light on this?
The problem started a month or two ago and is becoming very frequent. Normally when starting the engine from hot or cold the brake pedal can be depressed 15mm or so, you turn the key (should you be sensible enough to have one [sorry]), and the car starts. Now, after being left overnight I commonly find the brake pedal immovable. Either the engine doesn't turn over because it doesn't recognise the brake pedal as being pressed, or if the engine does turn over it just about staggers into life and then runs normally. If the brake pedal behaves normally in the morning then the car starts normally.
Time to head off to Audi no doubt but I am just curious if anything is known about this?
Thanks.

I should have added that as soon as the engine does start the pedal softens and sinks down to its normal foot pressure starting position.

Thanks V.