Because of the strong English currency, the pound.. coming to London is always costly. It is good that you save a good amount of cash if you are coming with no job and/or acommodation. Your inital expenses will cover:

TRANSPORT
To go house and job hunting you will have to use the public transport extensively, as the city is so big. This is also very expensive. Your best option is to acquire an Oyster card as soon as you land in the country. Read more about the public transport here.

MOBILE PHONE CARD
If you bring your own mobile phone, that will make your life easier, so long you have an "unlocked" handset. You can then buy a pre-paid card, as it will be almost impossible for you to get a contract until you have a place, a bank account and a job.

If you want to call home (abroad), then you can buy one of the many scratch calling cards with pin numbers to use from any public phone. These have excellent rates and will be useful.

FOOD
Until you sort a place, you will have to eat out. That is very very expensive unless you go for buffet-y type places.. or oriental restaurants (as well as kebabs, burgers and similars). Allow around £15-20/day in food and drink if you don't have a place to cook. Even though you can try eat cheap, we are talking about 3 meals a day, plus drinks.

INTERNET ACCESS
For job or house hunting, you will have to spend some time online. Most places charge a average of £1-£2/hour and there are plenty of places around town.

CLOTHING
Even if you are coming with a backpack, remember to bring a suit if you are looking for a job. Don't expect to buy one here if your budget is tight. Minimum prices are around £150-£200 for men. For women is always easier to find dressed up clothes at decent prices. Re the seasonal wearing, London has 4 seasons and that means you will need clothing and footwear for rain, hot sun, wind and cold. A bit of everything, basically.

If you have a good walk around the local (less cool) markets, you will be able to find plenty of bargains for basics: socks, underwear, etc... There are also plenty of discount shops and the city seems like it has Sales all year round. Just walk up and down Oxford Street and you will find plenty of things.

If your hotel's laundry service is expensive or if your first flat doesn't have a washing machine, there are plenty 'launderettes' too for your dirty clothes.

DISCOUNTS
If you are an student, make sure you bring your student card for great discounts. Try sort an International youth travel card if you can before you come.

If you join your local library, you will have access to many books, guides and internet for free or at a very cheap price. Even travelling guide books come in help, as you don't want to accummulate too many things or spend too much in books if you are here only temporarily.