Rupert Hargreaves owns no share mentioned. The Motley Fool UK has recommended AG Barr. Views expressed on the companies mentioned in this article are those of the writer and therefore may differ from the official recommendations we make in our subscription services such as Share Advisor, Hidden Winners and Pro. Here at The Motley Fool we believe that considering a diverse range of insights makes us better investors. The recent stock market rally has lifted many UK shares from their lows. However, this performance hasn’t discouraged me from buying equities. That’s because I’m following the approach billionaire investor Warren Buffett has refined over the past six decades.Warren Buffett-style investmentsWarren Buffett is a value investor at heart. But that doesn’t mean he’s not afraid to pay up for a high-quality business. In the past, he’s paid significant premiums for attractive equities.5G is here – and shares of this ‘sleeping giant’ could be a great way for you to potentially profit!According to one leading industry firm, the 5G boom could create a global industry worth US$12.3 TRILLION out of thin air…And if you click here we’ll show you something that could be key to unlocking 5G’s full potential…More often than not, these trades have paid off. This is why I’m planning to follow his approach with UK shares in the current stock market rally.The kinds of businesses I’m targeting for my portfolio are those I think Warren Buffett would want to buy. These include firms with an established brand presence, such as Irn-Bru producer A.G. Barr. While this business might not be a household name, Irn-Bru is, especially in Scotland.I see many similarities between this business and Warren Buffett’s core holding Coca-Cola in terms of brand strength and profit margins. Irn-Bru may not have the international recognition of the Coca-Cola brand but that hasn’t stopped the company from earning impressive returns for shareholders.It also has a strong track record of returning cash to investors. In the past, A.G. Barr has returned profits to investors with both dividends and share repurchase plans.Investing in the stock market rallyI’m also interested in tabletop gaming group Games Workshop. This company has a huge and dedicated fan base, which is willing to pay a premium to buy its products.Unfortunately, in the market rally, the stock, like many other UK shares, has increased rapidly in value.Some investors might be put off by these gains. However, I think it’s worth paying a premium to buy these kind of shares. The problem is, good quality businesses are very rarely marked down to discount valuations.This is something Warren Buffett has advised investors about in the past. “‘It’s far better to buy a wonderful company at a fair price than a fair company at a wonderful price,” he once said.In other words, these businesses might look a bit on the pricey side after their recent performance but, in my opinion, they’re wonderful companies. That suggests they’re worth buying for the long haul. Buffett’s track record stands testament that this strategy produces results in the long run.The bottom lineWarren Buffett’s most successful investments have been companies with an established market presence and devoted customer base. There aren’t many UK shares that tick these boxes, but I think the companies above do.By acquiring these stocks, and others like them, for my portfolio, I believe it’ll be possible to retire in comfort with a large financial nest egg. Simply click below to discover how you can take advantage of this. Stock market rally: I’m buying UK shares like Warren Buffett to retire in comfort Rupert Hargreaves | Thursday, 24th December, 2020 Enter Your Email Address Image source: Getty Images See all posts by Rupert Hargreaves I’m sure you’ll agree that’s quite the statement from Motley Fool Co-Founder Tom Gardner.But since our US analyst team first recommended shares in this unique tech stock back in 2016, the value has soared.What’s more, we firmly believe there’s still plenty of upside in its future. In fact, even throughout the current coronavirus crisis, its performance has been beating Wall St expectations.And right now, we’re giving you a chance to discover exactly what has got our analysts all fired up about this niche industry phenomenon, in our FREE special report, A Top US Share From The Motley Fool. 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