you will need 6wks for the deposit and a months rent in advance. If your work is bringing you over are they not offering a housing allowance? Most who do will pay the deposit too.
After tax you're looking at just under £3k per/month. In addition to rent you will have to pay council tax, I'd allow £100 a month. Your cable/internet estimate is low, but there are good deals all the time. We love Virgin Media, but not every area is cabled so you may be stuck getting your internet through your landline. I think BT is a bit of a rip and our last few places have done cable/internet/phone packages through Virgin. I think right now we pay about £45 a month plus any additional calls- to the US, etc.
Depending on where your office is, you can open up your search using the tube. When I worked in the city, I could walk to aldgate, tower hill and liverpool st within 5-12 mins. I wouldn't necessarily limit yourself to circle/district, I don't think making one change in the morning is really that big of a deal- or at least it wasn't to me!