LONDON -- This week, the blue-chip buying retail clients of stockbroker TD Direct Investing once again had some tempting blue-chip bargains in their sights. The fall in the price of BG Group, for instance, seems overdone. Lloyds Banking Group, too, as I wrote yesterday, looks to be on the mend.

So no wonder, then, that these two shares were respectively the broker's single-most popular and second-most popular 'buys' between the market's opening on Monday and today at noon. Equally, high-yield favourite Vodafone (LSE: VOD.L) shouldn't have surprised as the broker's third-most popular pick over the period.

But it's Barclays (LSE: BARC.L) (NYSE: BCS) that caught my eye as I ran down the list. The fourth-most popular "buy" over the week, the once-troubled bank has had a good three months, rising 27% over the period, while the FTSE 100 (UKX) has meandered along, falling 2%.

Consensus earnings estimate of 32 pence for the year -- and 36 pence for next year -- are a distinct improvement on last year's 25 pence, and are the best since 2008. So from that perspective, the bank would seem to have turned the corner, yet is still on a P/E of around 7. And while the forecast yield isn't great at 2.7%, Barclays is at least paying a dividend -- unlike Lloyds and Royal Bank of Scotland.

Just below Barclays in fourth place is oil giant BP (LSE: BP.L), which, like the banks, has had a torrid past few years, with the Gulf of Mexico disaster, Russia, oil refinery explosions, and boardroom upsets all featuring in the headlines. Yet, like a supertanker, BP ploughs on, delivering profits and dividends along the way.

On any metric, BP is still modestly rated, even though the dark days of 2010 and the 200 pence share price are long gone. On a forecast yield of 5.1%, and a forecast price-to-earnings (P/E) ratio of 7, a company that was once one of the very largest businesses in the FTSE 100 has undeniably fallen a long way. But the time to buy is when shares are cheap -- and BP today fits that criteria.

Further down the list -- much further down the list -- we find another beaten-down FTSE stalwart fallen on hard times: Aviva (LSE: AV.L), the 14th-most popular "buy" by the broker's clients between the market's opening on Monday and today at noon.

Granted, as with Barclays and BP, the accounts aren't a model of transparency. But anyone who has had anything to do with the business in recent years will recognize the characterization of its management by incoming chairman John McFarlane as "bureaucratic," and one of the first tasks of the new CEO -- when recruited -- will doubtless be to start shaking those bureaucrats up. Meanwhile, a forecast yield of 7.8%, and a P/E of just 6 go a long way to summarize Aviva's charms.

Finally, what did super-investors Neil Woodford and Warren Buffett buy this week? We can't tell you that, but we can tell you the names of the shares that they've been buying in the recent past -- and why they've been buying them.

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