They have started filming Apprentice 2013;
Via Twitter

Mon 25th Sept:
@NW3Gooner
They are filming the Apprentice in Camden Town
http://t.co/xbZkzcCq

http://t.co/8BNK4Csz

Tue 26th Sept:
‏@SpiceMarketLDN
Spotted outside Spice Market - new recruits filming for BBC1's Apprentice. Lots of shouting into Blackberries!

Wed 27th Sept:
@jackb09
Didn't expect to see the next #apprentice contestants filming in #canarywharf this morning
http://t.co/Ad356r0N

Thur 28th Sept:
@Johnny_Dubya
The apprentice filming at my brewery today. Might try and get on tv. #photobomb

Fri 29th Sept:
@shrimpcreek
They are filming the apprentice at the bricklayers putney and one of the teams are selling a ale called rhubarb & riches #realale #camra

@Sargeman
There filming an episode of the apprentice at the bricklayers in putney. Just seen Karen Brady #milf

@AndyNeilAndrew
I'm in a pub and they're filming the apprentice I just let them talk me in to buying a pint of rhubarb ale for £4.

@Amber_Candy
Just saw them filming the Apprentice on Southbank and bought the product!!!!

Tue 2nd Oct:
@KerrysWindow
They are filming The Apprentice on Shoreditch High Street. Boy in shiny suit came and grinned into my face...thought it was a stag do.

Wed 3rd Oct:
‏@AnjieDaden
Lol the Apprentice contestants r bin based in a house 4 doors down from my work. They have bn filming today

I presume it'll be broadcast from March-June next year like this year.

Hmm... Possibly first task? It looks like an all-blokes team. My guess is that it is either the standard "Sell a Product" first task or one similar to the condiments one earlier this year. Seems to be a "produce an ale, then sell it" task.

Sunday 7th October 2012
@_DonnaC
Apprentice filming on broadway market today... No sign of Nick and Karen though
http://t.co/MD0TaDCb

@jezzacave
New apprentice filming spotted!! Broadway market
http://t.co/3zLcr9qh

@wobblyclark
They're filming the Apprentice at Broadway Market today, 2 pop-up shops, and a bored looking Karren Brady

Looks like they started a week earlier then last year (twitter feeds from this year's candidates indicate that October 1 was their one year anniversary).