If you have good light from large windows it's great. If you don't have so much light, just crank up the ISO. I find that the 6D produces good results even upto ISO 10,000.
I'll see if I can dig out an example of an indoor shot taken with the 24-105 in natural light.
I find it's a great lens, 24mm is wide enough for landscapes and groups of people, 105mm is long enough to give nice portraits and compression.
If you do need really shallow depth of field and low light capabilities, then getting a 50mm f1.4 would solve that problem. You could easily get either the Canon 50mm f1.4 USM or a Sigma 50mm f1.4 EX DG (not the new Art) for £200ish and that would leave you £400ish for a 24-105 L.
If you're unsure, I'd suggest borrowing/hiring one for the weekend to give it a proper go. If nothing else, you have to be happy with the size, weight and usability.
Calumet in Central London will hire out a 24-105 for £20 per day:
http://calumetrental.co.uk/canon-ef-24-105mm-f4l-is-usm - might be worth the money to make sure you but the right lens for you.