When I add all the listed components up it comes to around £570, so it looks to me like you've forgotten to list your PSU. Let us know what it is so we know or we can suggest one.
If your not going to be gaming then you can use integrated video perfectly fine. Also you should try and order from as few sites as possible to save on delivery charges. AMD is probably the better route for being able to upgrade the CPU and cheaper for getting a motherboard that can do two ATI graphics cards. The i3 530 has an IGP so you could easily go that route to drop the graphics card. I'd say that the i3 530 would be a bit faster than a dual core Athlon, but with what I'm thinking you could get an AMD CPU that would be as fast/faster than the i3.
If you go onboard video then you can always add a video card later if it turns out you need one. I would suggest this motherboard for the onboard route: Asus M4A785TD-V Evo £72. You might even be able to afford one of the new 800 series chipsets with onboard so that next year or later you might be able to add a fast SSD.
I would stick with an AMD CPU, but from the saving from not having a graphics card then you should easily be able to afford a tri or quad core which will be much better at multi-tasking. I haven't read that many reviews of Asaka CPU coolers, but I know the Arctic Cooler has a good reputation for being quiet and it's quite cheap.
This build would be perfectly adequate at the lower end of your budget. If you went to the top end of your budget you could get a faster quad core, which would be even faster at your tasks, you could get a 800 series chipset (probably 890GX) with onboard video and SATA 6Gbps/USB3, maybe a power supply that could more easily accommodate a graphics card if you wanted to add one at any point, maybe a nicer case - the Antec 300 is a very nice budget case, maybe a nicer monitor. I don't think you would be able to make all of those changes, so you would have to decide if you wanted to spend up to £600 and then which of those things would be most important/appealing to you.