UK shares have kick-started the year in awesome fashion. The FTSE 100 has rallied 6.9%. The FTSE 250 has also been getting in on the action, climbing 6%.

But plenty of UK-listed companies still look like bargains, in my eyes. The average Footsie price-to-earnings (P/E) ratio is just 11. That’s far off from its historical average of between 14 and 15.

What’s in store?

It’s been a tough few years for retail traders. The pandemic was a once-in-a-lifetime occurrence that sent stock markets across the globe tumbling. The record inflation and interest rate hikes that have followed haven’t been much more fun. But it seems we may be finally coming out the other side.

I’m aware the issues above could still hinder the Footsie’s performance this year. While it’s widely rumoured the first rate cut will occur in August, should the Bank of England decide to delay this, that would no doubt see markets react negatively. Of course, I can’t forget there’s the upcoming election to throw into the current cocktail of uncertainty too.

But while the UK will face challenges, looking at the valuation of many businesses, I’m hopeful in the years to come we could see share price continue to tick upwards. Plenty of UK shares look severely undervalued right now. For investors who pick stocks for the long run, now could be a great opportunity to dive in and snap up some bargains.

A great stock?

One example of a stock I’m hoping to pick up in the near future is Unilever (LSE: ULVR). It has put up a brilliant performance this year. So far, it’s jumped 14.6%. Even so, trading with a P/E of just below 20, I still think there’s value in its shares. That’s below its historical average.

I’m bullish on the growth opportunities the stock could provide. Under CEO Hein Schumacher, the firm’s making progress with its streamlining mission. Schumacher wants to build a business that can “do fewer things better”. In an attempt to focus more on its core brands, Unilever’s been offloading its underperforming and capital-intensive units.

It’s also a defensive stock. That means through periods of uncertainty, it can bring stability to my portfolio. There should always be demand for the essential goods it sells.

That said, it does sell premium brands. This means that competition’s a threat as consumers may shop around for cheaper alternatives. That’s especially pertinent during a cost-of-living crisis.

But I’m still a fan today. And with its 3.4% dividend yield, there’s the opportunity to generate some extra cash through buying shares. That’s by no means the best yield on the Footsie. But it hasn’t cut its payout for over 50 years, which is an incredible record.

Barclays recently slapped a 5,200p price target on the stock. That represents an 18.7% premium to its current price. With that in mind, I think June could be a smart time for investors to consider looking at cheap UK shares.