should? no, they have no obligation to lend you one.
might they? perhaps, but it won't be free. my mini dealer uses some car rental company to keep up with loaner cars because they minis don't stand around long enough to be loaners ... so if you need a loaner car at my us dealer when your mini's in the shop, even then you have to pay a little bit.
call them and ask if they have any options, and also check, if you really need a car in the meantime, with some car rental places. they often do really deep discount if you're renting a car for more than 2 weeks.
Depends on the relationship you have with the dealer...
When i got an RX8 a couple of years back I said I'd be without a car for a week as I'd sold my MINI on. they had no problem with that and lent me a mazda 3 until my car arrived.
Audi also will lend you a car if they don't meet the original quoted delivery date. My TT was late by three days, but I declined a loan car as I had my MINI to use too.