Dear Caleb,
Let me take a shot at some answers. You don't say so but I am going to assume that you are young and single, because you haven't asked about family issues on relocation.
1. Where is the best place to find a flat if my office is at 103 Wigmore Street London?
London has fairly good public transport; by and large, Londoners do not live near to their placed of work. The nearest Underground (MRT) station to your office is Bond Street which is in easy walking distance and is served by the Central and Jubilee lines. There are a number of attractive suburbs served by the Jubilee Line which stops at Bond Street - Canary Wharf would put you in a sizeable East Asian community in financial services, for example. Alternatively you can look at the Holland Park area on the Central Line to the West.
2. How much is the average rent per month for a decent 1 bedroom flat near my work area?
Don't plan on living near your work area; its in the West End and flats are fearsomely expensive there.
3. How much is the average daily/monthly expense for a single guy?
You will be able to live very comfortably on your salary; its more than most of us here get.
4. Is GBP 80,000 annual salary enough for me to live and save in London? I am a bit hesitant in getting the new role from my company as I know that London is charging 40% tax, I might not be able to save :(.
Yes, but you will need to take some advice on the best way to save - the UK does not have anything like Singapore's excellent CPF, but you may well be able to make Additional Voluntary Contributions into a pension - these are tax free but there may be restrictions on taking the pension out of the country. You should get advice on this.