you wont be able to place an order normally until you get your letter from motability usually about 3 months before the end of the lease. but a dealer should allow test drives etc at any time. i spent quite a bit of time beginning 6 months in advance test driving various models as i have a back problem so i need a higher seat and one that will adjust to suit so i test drove about 8 different cars.some of them more than once, mini even gave me one for 24hrs.
in the end i got it down to the bmw i3 and the mini countryman going with mini as they had a £500 cashback/ap contribution whereas bmw wouldnt offer anything.
if your set on the one series i would canvas several dealers for the best deal but all of them should give you a test drive whenever you want one. very poor customer service if they wont.