Tokina 11-16 f/2.8 may be your best bet (around £400ish). They also do a 12-24 f/4 which could be ok too (£350ish).
The sigma wouldn't be very good at low light, it's too slow really.
Anyone remember the old rule regarding speeds that you can hand hold on,the Sigma is an equivalent 16mm so you should be able to hand hold at 15th of a second and with practice 8th of a second
So dont worry about half a stop worry about how the lens looks and feels in your hand.