The U.K. economy is struggling to avoid a triple-dip recession, the British mortgage market is moribund and regulators say its banks need to raise more capital lest another epic financial crisis tear their balance sheets down.

Then there’s the parade of scandals (fixing interest rates, anyone?) that make the shenanigans of U.S. bankers almost seem like small beer.

But despite all this, a survey of the big British money center banks reveals a few compelling investing ideas — including a dependable dividend machine and a cost-cutting turnaround play. Then again, it also shows a storied name where the easy money looks to have already been made.

With that in mind, let’s take a closer look at two British bank stocks to buy and one to sell.

HSBC

It’s boring, it’s sleepy, it has weak loan growth, low revenue growth and declining net interest margins (the difference between what it makes on loans and pays on loans). Yet shares in HSBC (NYSE:HBC) are up 20% over the last 52 weeks, beating the S&P 500 by 7 percentage points.

HSBC has been shedding assets around the globe, making the bank more focused and less risky. It sold or shuttered 47 businesses amid a three-year restructuring plan and slashed an astonishing 38,000 jobs.

No, that’s not going to do much for top-line growth in the short run, but who cares as long as it keeps churning out — and hiking — its payouts?

“HSBC’s interim dividend payments are a bit lumpy, but the trailing yield still gives you a nice yield of 4.4% … and those payouts are forecast keep rising at a double-digit percent rate. As Investec analyst Ian Gordon writes in a recent note to clients:

“Whereas bank specialists typically seek to identify superior opportunities elsewhere in the sector, HSBC remains the perennial ‘generalists’ favourite bank’. The dividend probably plays an important role here, and in our view, HSBC’s dividend-paying capacity is not in question. Indeed, we forecast (above consensus) dividend growth of 15%-16% [annually] through 2013/14.”

Barclays

The bank at the center of the rate-fixing scandal had a turbulent 2012. But a funny thing happened amid Barclays (NYSE:BCS) booting its top brass and paying a nearly half-billion-dollar fine: The stock went on a tear, rising 27% over the last 52 weeks.

Like HSBC, Barclays is pulling in its reins, shedding assets, operations and employees at a torrid pace. But what’s bad news for labor is usually good news for capital — and that’s certainly been the case here.

A slash-and-burn policy on the bank’s cost structure is expected to send profits shooting higher as revenue goes essentially nowhere.

Earnings per share, excluding special items and charges, are forecast to increase 27% this year and 15% in 2014. Longer term, analysts figure Barclays can grow earnings at an average annual rate of nearly 20% over the next five years — well ahead of the broader market.

Just as important, Barclays pays a generous, stable dividend, good for a trailing yield of 2.3%. Additionally, shares appear to be adequately discounted for risk. The stock trades at a price-to-book value of 0.6, which is in line with U.S. turnaround stories like Bank of America (NYSE:BAC) and Citigroup (NYSE:C).

Lloyds

Where HSBC and Barclays are still positive for the year, Lloyds (NYSE:LYG) is down nearly 10%, hurt by unrelenting weakness in the U.K. economy.

Ordinarily, a pullback like this might have you looking to buy on weakness, but this stock is still hanging on to a remarkable 50% rise over the last 52 weeks, suggesting that the easy money has been more than made.

Unlike HSBC or Barclays, which still have sprawling international revenue streams despite their retrenching, Lloyds is much more a play on the domestic U.K. economy.

That’s not good.

The British housing market, as measured by mortgage approvals and lending data, has been terrible so far this year. The wider is economy isn’t doing much better. Amid such weakness, you’d do better to bet on banks with overseas revenue streams like HSBC and BCS. As Investec’s Gordon writes in a recent note to clients:

“Revenues, profitability and returns are likely to remain under significant pressure for the U.K. banks in 2013, and we reaffirm our preference for the more internationally exposed banks.”

Furthermore, Lloyds suspended its dividend four years ago and has taken a resumption in payouts off the table until next year at the earliest.

Given the weak state of the U.K. economy, lack of dividend and huge run up in share price over the past year, you’d best avoid Lloyds when considering the big British bank stocks.

As of this writing, Dan Burrows did not hold positons in any of the aforementioned securities.