When renting housing you'll need to pay a deposit - typically 6 weeks rent - and probably agents fees(for references, inventory). Maybe your husband's company could help you with that one?
Try to get a property with decent insulation i.e. double glazing and loft insulation and a modern gas combi boiler. It'll save loads on your energy bills (or use the lack of it to haggle down your rent)
Hammersmith is well served with Tube lines and buses, so no problem there. Public transport is very safe to use (many's the time I've come home over refreshed late on my own and never worried about it)
Don't think anyone has mentioned phone/cable/internet? You'll need a TV licence - £146.50 per year, a basic package should cost about £20 per month for free evening and weekend calls plus internet and tv. You can probably get it cheaper if you're not bothered about the tv channels (there are plenty on Freeview)
I'd get a local mobile phone - pay as you go would be £5-£10 per month.
Healthcare - I assume (if you're not paying tax in this country) that you won't be entitled to free treatment on the National Health Service. Hopefully you'll get insurance through work? If you have a minor accident (needing stitches, for example) you will get treated for free at the hospital emergency department. The NHS only start charging when you have to stay in (they treat you and bill later) but you'll have to pay for drugs.
Eating out can be expensive but it's not hard to find 2 for 1 deals and happy hours. Similarly with the cinema(there is one in Hammersmith).
Other great things about London - you can get the train to France in just over two hours, great parks, multi-cultural.
Do come over if you can make the numbers work. You won't regret it.