Yes, you get a say.
In terms of the system at Pembroke, everyone is given a form where they have to indicate the order of preference for each of the different accommodation blocks (you're told about the price and facilities of each). You might find that you don't get your first choice so that everyone can be accommodated, even in cases where you wouldn't expect it.
For instance, you're also asked about the maximum you'd be willing to pay for accommodation. Suppose you're like me and you'd prefer to live in the oldest buildings (
) - since those rooms are smaller, they're likely to be less expensive. However, you say that you'd be willing to pay up to the cost of the second highest band of accommodation. You might find yourself in a more expensive room lower on your preferences so that someone who can only afford an "old" room can have the one you wanted.
On that basis, it's worth bearing in mind that you can complete the form strategically to improve your chances. I didn't want to live in Foundress Court, the newest accommodation and the most expensive, so I said I wouldn't be willing to pay that much for my room. That way, I knew I couldn't be living in Foundress.