They won't change their mind. That's the only offer you will get. Things will sort out after 4 weeks anyway and you will be in single rooms. Westwood sharing is only temporary. You or someone else will move out either to another place on campus or off campus.
Warwick have set targets when it comes to offers. The number of places offered can't simply be limited by the number of places on campus. Second years have to live off campus. Some final years have to live off campus.
If everyone had to live on campus then Warwick will be 6 times smaller than it is now.
Warwick Accommodation has come up with solutions in order to deal with this situation. They add an additional 75 places on campus as a reserve (150 people share rooms in Westwood). Some of these 75 people will then take up places at empty/no shows in other rooms on campus. The rest will be offered off campus accommodation. There are then 150 off campus places at Liberty Park, a hall shared with Cov uni students. The rest then will have to live off campus in smaller houses.
There is an allocation system in place to try and give accommodation fairly. There are 4 priority groups:
1) Medical reasons mean they are top priority.
2) Firm Warwick and apply for accommodation by 31st July, meet the offer by 31st August.
3) Insure Warwick and apply for accommodation by 31st July, meet the offer by 31st August.
4) Apply after 31st July, miss offer and come in via clearing, etc.
If the places on campus fills up by group 3, a random ballot is used to determine if you are on or off campus. Group 4 is done on a first come, first served basis.
All this information would have been available when you apply: WA has a strategy and policy here:
http://www2.warwick.ac.uk/services/accommodation/studentaccommodation/all/campus/accommodation_strategy_and_policy.pdf